diff --git a/Library/Homebrew/bundle_version.rb b/Library/Homebrew/bundle_version.rb
index ca63aa36b8..69abe5cfbd 100644
--- a/Library/Homebrew/bundle_version.rb
+++ b/Library/Homebrew/bundle_version.rb
@@ -59,7 +59,7 @@ module Homebrew
         [other.version, other.short_version].map { |v| v&.yield_self(&Version.public_method(:new)) }
     end
 
-    # Create a nicely formatted version (on a best effor basis).
+    # Create a nicely formatted version (on a best effort basis).
     sig { returns(String) }
     def nice_version
       nice_parts.join(",")
diff --git a/Library/Homebrew/cask/audit.rb b/Library/Homebrew/cask/audit.rb
index 0e54c062dd..6121c1ac00 100644
--- a/Library/Homebrew/cask/audit.rb
+++ b/Library/Homebrew/cask/audit.rb
@@ -298,7 +298,7 @@ module Cask
     end
 
     def check_hosting_with_appcast
-      return if cask.appcast
+      return if cask.appcast || cask.livecheckable?
 
       add_appcast = "please add an appcast. See https://github.com/Homebrew/homebrew-cask/blob/HEAD/doc/cask_language_reference/stanzas/appcast.md"
 
diff --git a/Library/Homebrew/livecheck.rb b/Library/Homebrew/livecheck.rb
index 7fb6c3bb2b..43288cdb3c 100644
--- a/Library/Homebrew/livecheck.rb
+++ b/Library/Homebrew/livecheck.rb
@@ -8,6 +8,8 @@
 # This information is used by the `brew livecheck` command to control its
 # behavior.
 class Livecheck
+  extend Forwardable
+
   # A very brief description of why the formula/cask is skipped (e.g. `No longer
   # developed or maintained`).
   # @return [String, nil]
@@ -67,7 +69,9 @@ class Livecheck
   #
   # @param symbol [Symbol] symbol for the desired strategy
   # @return [Symbol, nil]
-  def strategy(symbol = nil)
+  def strategy(symbol = nil, &block)
+    @strategy_block = block if block
+
     case symbol
     when nil
       @strategy
@@ -78,6 +82,8 @@ class Livecheck
     end
   end
 
+  attr_reader :strategy_block
+
   # Sets the `@url` instance variable to the provided argument or returns the
   # `@url` instance variable when no argument is provided. The argument can be
   # a `String` (a URL) or a supported `Symbol` corresponding to a URL in the
@@ -103,6 +109,9 @@ class Livecheck
     end
   end
 
+  delegate version: :@formula_or_cask
+  private :version
+
   # Returns a `Hash` of all instance variable values.
   # @return [Hash]
   def to_hash
diff --git a/Library/Homebrew/livecheck/error.rb b/Library/Homebrew/livecheck/error.rb
new file mode 100644
index 0000000000..a10875551b
--- /dev/null
+++ b/Library/Homebrew/livecheck/error.rb
@@ -0,0 +1,12 @@
+# typed: true
+# frozen_string_literal: true
+
+module Homebrew
+  module Livecheck
+    # Error during a livecheck run.
+    #
+    # @api private
+    class Error < RuntimeError
+    end
+  end
+end
diff --git a/Library/Homebrew/livecheck/livecheck.rb b/Library/Homebrew/livecheck/livecheck.rb
index 9025a1fb1e..ece9c04656 100644
--- a/Library/Homebrew/livecheck/livecheck.rb
+++ b/Library/Homebrew/livecheck/livecheck.rb
@@ -1,6 +1,7 @@
 # typed: false
 # frozen_string_literal: true
 
+require "livecheck/error"
 require "livecheck/strategy"
 require "ruby-progressbar"
 require "uri"
@@ -30,6 +31,7 @@ module Homebrew
     STRATEGY_SYMBOLS_TO_SKIP_PREPROCESS_URL = [
       :github_latest,
       :page_match,
+      :sparkle,
     ].freeze
 
     UNSTABLE_VERSION_KEYWORDS = %w[
@@ -144,7 +146,7 @@ module Homebrew
 
         if latest.blank?
           no_versions_msg = "Unable to get versions"
-          raise TypeError, no_versions_msg unless json
+          raise Livecheck::Error, no_versions_msg unless json
 
           next version_info if version_info.is_a?(Hash) && version_info[:status] && version_info[:messages]
 
@@ -200,6 +202,7 @@ module Homebrew
           status_hash(formula_or_cask, "error", [e.to_s], full_name: full_name, verbose: verbose)
         elsif !quiet
           onoe "#{Tty.blue}#{formula_or_cask_name(formula_or_cask, full_name: full_name)}#{Tty.reset}: #{e}"
+          $stderr.puts e.backtrace if debug && !e.is_a?(Livecheck::Error)
           nil
         end
       end
@@ -268,6 +271,7 @@ module Homebrew
     # @return [Hash, nil, Boolean]
     def skip_conditions(formula_or_cask, json: false, full_name: false, quiet: false, verbose: false)
       formula = formula_or_cask if formula_or_cask.is_a?(Formula)
+      cask = formula_or_cask if formula_or_cask.is_a?(Cask::Cask)
 
       if formula&.deprecated? && !formula.livecheckable?
         return status_hash(formula, "deprecated", full_name: full_name, verbose: verbose) if json
@@ -276,6 +280,13 @@ module Homebrew
         return
       end
 
+      if cask&.discontinued? && !cask.livecheckable?
+        return status_hash(cask, "discontinued", full_name: full_name, verbose: verbose) if json
+
+        puts "#{Tty.red}#{cask_name(cask, full_name: full_name)}#{Tty.reset} : discontinued" unless quiet
+        return
+      end
+
       if formula&.disabled? && !formula.livecheckable?
         return status_hash(formula, "disabled", full_name: full_name, verbose: verbose) if json
 
@@ -290,6 +301,20 @@ module Homebrew
         return
       end
 
+      if cask&.version&.latest? && !cask.livecheckable?
+        return status_hash(cask, "latest", full_name: full_name, verbose: verbose) if json
+
+        puts "#{Tty.red}#{cask_name(cask, full_name: full_name)}#{Tty.reset} : latest" unless quiet
+        return
+      end
+
+      if cask&.url&.unversioned? && !cask.livecheckable?
+        return status_hash(cask, "unversioned", full_name: full_name, verbose: verbose) if json
+
+        puts "#{Tty.red}#{cask_name(cask, full_name: full_name)}#{Tty.reset} : unversioned" unless quiet
+        return
+      end
+
       if formula&.head_only? && !formula.any_version_installed?
         head_only_msg = "HEAD only formula must be installed to be livecheckable"
         return status_hash(formula, "error", [head_only_msg], full_name: full_name, verbose: verbose) if json
@@ -412,9 +437,9 @@ module Homebrew
 
       has_livecheckable = formula_or_cask.livecheckable?
       livecheck = formula_or_cask.livecheck
+      livecheck_url = livecheck.url
       livecheck_regex = livecheck.regex
       livecheck_strategy = livecheck.strategy
-      livecheck_url = livecheck.url
 
       urls = [livecheck_url] if livecheck_url.present?
       urls ||= checkable_urls(formula_or_cask)
@@ -452,7 +477,9 @@ module Homebrew
         strategies = Strategy.from_url(
           url,
           livecheck_strategy: livecheck_strategy,
+          url_provided:       livecheck_url.present?,
           regex_provided:     livecheck_regex.present?,
+          block_provided:     livecheck.strategy_block.present?,
         )
         strategy = Strategy.from_symbol(livecheck_strategy)
         strategy ||= strategies.first
@@ -467,8 +494,13 @@ module Homebrew
           puts "Regex:            #{livecheck_regex.inspect}" if livecheck_regex.present?
         end
 
-        if livecheck_strategy == :page_match && livecheck_regex.blank?
-          odebug "#{strategy_name} strategy requires a regex"
+        if livecheck_strategy == :page_match && (livecheck_regex.blank? && livecheck.strategy_block.blank?)
+          odebug "#{strategy_name} strategy requires a regex or block"
+          next
+        end
+
+        if livecheck_strategy.present? && livecheck_url.blank?
+          odebug "#{strategy_name} strategy requires a url"
           next
         end
 
@@ -479,7 +511,7 @@ module Homebrew
 
         next if strategy.blank?
 
-        strategy_data = strategy.find_versions(url, livecheck_regex)
+        strategy_data = strategy.find_versions(url, livecheck_regex, &livecheck.strategy_block)
         match_version_map = strategy_data[:matches]
         regex = strategy_data[:regex]
 
diff --git a/Library/Homebrew/livecheck/strategy.rb b/Library/Homebrew/livecheck/strategy.rb
index 4115432951..c999fce0d3 100644
--- a/Library/Homebrew/livecheck/strategy.rb
+++ b/Library/Homebrew/livecheck/strategy.rb
@@ -57,12 +57,12 @@ module Homebrew
       # @param regex_provided [Boolean] whether a regex is provided in the
       #   `livecheck` block
       # @return [Array]
-      def from_url(url, livecheck_strategy: nil, regex_provided: nil)
+      def from_url(url, livecheck_strategy: nil, url_provided: nil, regex_provided: nil, block_provided: nil)
         usable_strategies = strategies.values.select do |strategy|
           if strategy == PageMatch
             # Only treat the `PageMatch` strategy as usable if a regex is
             # present in the `livecheck` block
-            next unless regex_provided
+            next unless regex_provided || block_provided
           elsif strategy.const_defined?(:PRIORITY) &&
                 !strategy::PRIORITY.positive? &&
                 from_symbol(livecheck_strategy) != strategy
@@ -80,6 +80,49 @@ module Homebrew
           (strategy.const_defined?(:PRIORITY) ? -strategy::PRIORITY : -DEFAULT_PRIORITY)
         end
       end
+
+      def self.page_headers(url)
+        @headers ||= {}
+
+        return @headers[url] if @headers.key?(url)
+
+        headers = []
+
+        [:default, :browser].each do |user_agent|
+          args = [
+            "--head",                 # Only work with the response headers
+            "--request", "GET",       # Use a GET request (instead of HEAD)
+            "--silent",               # Silent mode
+            "--location",             # Follow redirects
+            "--connect-timeout", "5", # Max time allowed for connection (secs)
+            "--max-time", "10"        # Max time allowed for transfer (secs)
+          ]
+
+          stdout, _, status = curl_with_workarounds(
+            *args, url,
+            print_stdout: false, print_stderr: false,
+            debug: false, verbose: false,
+            user_agent: user_agent, retry: false
+          )
+
+          while stdout.match?(/\AHTTP.*\r$/)
+            h, stdout = stdout.split("\r\n\r\n", 2)
+
+            headers << h.split("\r\n").drop(1)
+                        .map { |header| header.split(/:\s*/, 2) }
+                        .to_h.transform_keys(&:downcase)
+          end
+
+          return (@headers[url] = headers) if status.success?
+        end
+
+        headers
+      end
+
+      def self.page_content(url)
+        @page_content ||= {}
+        @page_content[url] ||= URI.parse(url).open.read
+      end
     end
   end
 end
@@ -92,9 +135,11 @@ require_relative "strategy/github_latest"
 require_relative "strategy/gnome"
 require_relative "strategy/gnu"
 require_relative "strategy/hackage"
+require_relative "strategy/header_match"
 require_relative "strategy/launchpad"
 require_relative "strategy/npm"
 require_relative "strategy/page_match"
 require_relative "strategy/pypi"
 require_relative "strategy/sourceforge"
+require_relative "strategy/sparkle"
 require_relative "strategy/xorg"
diff --git a/Library/Homebrew/livecheck/strategy/header_match.rb b/Library/Homebrew/livecheck/strategy/header_match.rb
new file mode 100644
index 0000000000..22d3ea7e49
--- /dev/null
+++ b/Library/Homebrew/livecheck/strategy/header_match.rb
@@ -0,0 +1,78 @@
+# typed: false
+# frozen_string_literal: true
+
+require_relative "page_match"
+
+module Homebrew
+  module Livecheck
+    module Strategy
+      # The {HeaderMatch} strategy follows all URL redirections and scans
+      # the resulting headers for matching text using the provided regex.
+      #
+      # @api private
+      class HeaderMatch
+        extend T::Sig
+
+        NICE_NAME = "Header match"
+
+        # A priority of zero causes livecheck to skip the strategy. We only
+        # apply {HeaderMatch} using `strategy :header_match` in a `livecheck`
+        # block, as we can't automatically determine when this can be
+        # successfully applied to a URL.
+        PRIORITY = 0
+
+        # The `Regexp` used to determine if the strategy applies to the URL.
+        URL_MATCH_REGEX = %r{^https?://}i.freeze
+
+        # Whether the strategy can be applied to the provided URL.
+        # The strategy will technically match any HTTP URL but is
+        # only usable with a `livecheck` block containing a regex
+        # or block.
+        sig { params(url: String).returns(T::Boolean) }
+        def self.match?(url)
+          URL_MATCH_REGEX.match?(url)
+        end
+
+        # Checks the final URL for new versions after following all redirections,
+        # using the provided regex for matching.
+        sig { params(url: String, regex: T.nilable(Regexp)).returns(T::Hash[Symbol, T.untyped]) }
+        def self.find_versions(url, regex, &block)
+          match_data = { matches: {}, regex: regex, url: url }
+
+          headers = Strategy.page_headers(url)
+
+          # Merge the headers from all responses into one hash
+          merged_headers = headers.reduce(&:merge)
+
+          if block
+            match = block.call(merged_headers)
+          else
+            match = nil
+
+            if (filename = merged_headers["content-disposition"])
+              if regex
+                match ||= filename[regex, 1]
+              else
+                v = Version.parse(filename, detected_from_url: true)
+                match ||= v.to_s unless v.null?
+              end
+            end
+
+            if (location = merged_headers["location"])
+              if regex
+                match ||= location[regex, 1]
+              else
+                v = Version.parse(location, detected_from_url: true)
+                match ||= v.to_s unless v.null?
+              end
+            end
+          end
+
+          match_data[:matches][match] = Version.new(match) if match
+
+          match_data
+        end
+      end
+    end
+  end
+end
diff --git a/Library/Homebrew/livecheck/strategy/page_match.rb b/Library/Homebrew/livecheck/strategy/page_match.rb
index 49961eff59..361cf04b97 100644
--- a/Library/Homebrew/livecheck/strategy/page_match.rb
+++ b/Library/Homebrew/livecheck/strategy/page_match.rb
@@ -30,8 +30,8 @@ module Homebrew
         URL_MATCH_REGEX = %r{^https?://}i.freeze
 
         # Whether the strategy can be applied to the provided URL.
-        # PageMatch will technically match any HTTP URL but it's only usable
-        # when the formula has a `livecheck` block containing a regex.
+        # PageMatch will technically match any HTTP URL but is only
+        # usable with a `livecheck` block containing a regex.
         #
         # @param url [String] the URL to match against
         # @return [Boolean]
@@ -46,10 +46,28 @@ module Homebrew
         # @param regex [Regexp] a regex used for matching versions in the
         #   content
         # @return [Array]
-        def self.page_matches(url, regex)
-          page = URI.parse(url).open.read
-          matches = page.scan(regex)
-          matches.map(&:first).uniq
+        def self.page_matches(url, regex, &block)
+          page = Strategy.page_content(url)
+
+          if block
+            case (value = block.call(page))
+            when String
+              return [value]
+            when Array
+              return value
+            else
+              raise TypeError, "Return value of `strategy :page_match` block must be a string or array of strings."
+            end
+          end
+
+          page.scan(regex).map do |match|
+            case match
+            when String
+              match
+            else
+              match.first
+            end
+          end.uniq
         end
 
         # Checks the content at the URL for new versions, using the provided
@@ -58,10 +76,10 @@ module Homebrew
         # @param url [String] the URL of the content to check
         # @param regex [Regexp] a regex used for matching versions in content
         # @return [Hash]
-        def self.find_versions(url, regex)
+        def self.find_versions(url, regex, &block)
           match_data = { matches: {}, regex: regex, url: url }
 
-          page_matches(url, regex).each do |match|
+          page_matches(url, regex, &block).each do |match|
             match_data[:matches][match] = Version.new(match)
           end
 
diff --git a/Library/Homebrew/livecheck/strategy/sparkle.rb b/Library/Homebrew/livecheck/strategy/sparkle.rb
new file mode 100644
index 0000000000..63d61a9a9e
--- /dev/null
+++ b/Library/Homebrew/livecheck/strategy/sparkle.rb
@@ -0,0 +1,109 @@
+# typed: true
+# frozen_string_literal: true
+
+require "bundle_version"
+require_relative "page_match"
+
+module Homebrew
+  module Livecheck
+    module Strategy
+      # The {Sparkle} strategy fetches content at a URL and parses
+      # it as a Sparkle appcast in XML format.
+      #
+      # @api private
+      class Sparkle
+        extend T::Sig
+
+        # A priority of zero causes livecheck to skip the strategy. We only
+        # apply {Sparkle} using `strategy :sparkle` in a `livecheck` block,
+        # as we can't automatically determine when this can be successfully
+        # applied to a URL without fetching the content.
+        PRIORITY = 0
+
+        # The `Regexp` used to determine if the strategy applies to the URL.
+        URL_MATCH_REGEX = %r{^https?://}i.freeze
+
+        # Whether the strategy can be applied to the provided URL.
+        # The strategy will technically match any HTTP URL but is
+        # only usable with a `livecheck` block containing a regex
+        # or block.
+        sig { params(url: String).returns(T::Boolean) }
+        def self.match?(url)
+          URL_MATCH_REGEX.match?(url)
+        end
+
+        Item = Struct.new(:title, :url, :bundle_version, :short_version, :version, keyword_init: true) do
+          extend T::Sig
+
+          extend Forwardable
+
+          delegate version: :bundle_version
+          delegate short_version: :bundle_version
+        end
+
+        sig { params(content: String).returns(T.nilable(Item)) }
+        def self.item_from_content(content)
+          require "nokogiri"
+
+          xml = Nokogiri::XML(content)
+          xml.remove_namespaces!
+
+          items = xml.xpath("//rss//channel//item").map do |item|
+            enclosure = (item > "enclosure").first
+
+            url = enclosure&.attr("url")
+            short_version = enclosure&.attr("shortVersionString")
+            version = enclosure&.attr("version")
+
+            url ||= (item > "link").first&.text
+            short_version ||= (item > "shortVersionString").first&.text&.strip
+            version ||= (item > "version").first&.text&.strip
+
+            title = (item > "title").first&.text&.strip
+
+            if match = title&.match(/(\d+(?:\.\d+)*)\s*(\([^)]+\))?\Z/)
+              short_version ||= match[1]
+              version ||= match[2]
+            end
+
+            bundle_version = BundleVersion.new(short_version, version) if short_version || version
+
+            data = {
+              title:          title,
+              url:            url,
+              bundle_version: bundle_version,
+              short_version:  bundle_version&.short_version,
+              version:        bundle_version&.version,
+            }.compact
+
+            Item.new(**data) unless data.empty?
+          end.compact
+
+          items.max_by(&:bundle_version)
+        end
+
+        # Checks the content at the URL for new versions.
+        sig { params(url: String, regex: T.nilable(Regexp)).returns(T::Hash[Symbol, T.untyped]) }
+        def self.find_versions(url, regex, &block)
+          raise ArgumentError, "The #{T.must(name).demodulize} strategy does not support a regex." if regex
+
+          match_data = { matches: {}, regex: regex, url: url }
+
+          content = Strategy.page_content(url)
+
+          if (item = item_from_content(content))
+            match = if block
+              block.call(item)&.to_s
+            else
+              item.bundle_version&.nice_version
+            end
+
+            match_data[:matches][match] = Version.new(match) if match
+          end
+
+          match_data
+        end
+      end
+    end
+  end
+end
diff --git a/Library/Homebrew/test/livecheck/livecheck_spec.rb b/Library/Homebrew/test/livecheck/livecheck_spec.rb
index 5873f7ae78..a4cdb6bc4b 100644
--- a/Library/Homebrew/test/livecheck/livecheck_spec.rb
+++ b/Library/Homebrew/test/livecheck/livecheck_spec.rb
@@ -20,6 +20,24 @@ describe Homebrew::Livecheck do
     end
   end
 
+  let(:c) do
+    Cask::CaskLoader.load(+<<-RUBY)
+      cask "test" do
+        version "0.0.1,2"
+
+        url "https://brew.sh/test-0.0.1.tgz"
+        name "Test"
+        desc "Test cask"
+        homepage "https://brew.sh"
+
+        livecheck do
+          url "https://formulae.brew.sh/api/formula/ruby.json"
+          regex(/"stable":"(\d+(?:\.\d+)+)"/i)
+        end
+      end
+    RUBY
+  end
+
   let(:f_deprecated) do
     formula("test_deprecated") do
       desc "Deprecated test formula"
@@ -29,6 +47,24 @@ describe Homebrew::Livecheck do
     end
   end
 
+  let(:c_discontinued) do
+    Cask::CaskLoader.load(+<<-RUBY)
+      cask "test_discontinued" do
+        version "0.0.1"
+        sha256 :no_check
+
+        url "https://brew.sh/test-0.0.1.tgz"
+        name "Test Discontinued"
+        desc "Discontinued test cask"
+        homepage "https://brew.sh"
+
+        caveats do
+          discontinued
+        end
+      end
+    RUBY
+  end
+
   let(:f_disabled) do
     formula("test_disabled") do
       desc "Disabled test formula"
@@ -38,11 +74,39 @@ describe Homebrew::Livecheck do
     end
   end
 
-  let(:f_gist) do
-    formula("test_gist") do
-      desc "Gist test formula"
+  let(:f_versioned) do
+    formula("test@0.0.1") do
+      desc "Versioned test formula"
+      homepage "https://brew.sh"
+      url "https://brew.sh/test-0.0.1.tgz"
+    end
+  end
+
+  let(:c_latest) do
+    Cask::CaskLoader.load(+<<-RUBY)
+      cask "test_latest" do
+        version :latest
+        sha256 :no_check
+
+        url "https://brew.sh/test-0.0.1.tgz"
+        name "Test Latest"
+        desc "Latest test cask"
+        homepage "https://brew.sh"
+      end
+    RUBY
+  end
+
+  # `URL#unversioned?` doesn't work properly when using the
+  # `Cask::CaskLoader.load` setup above, so we use `Cask::Cask.new` instead.
+  let(:c_unversioned) do
+    Cask::Cask.new "test_unversioned" do
+      version "1.2.3"
+      sha256 :no_check
+
+      url "https://brew.sh/test.tgz"
+      name "Test Unversioned"
+      desc "Unversioned test cask"
       homepage "https://brew.sh"
-      url "https://gist.github.com/Homebrew/0000000000"
     end
   end
 
@@ -54,6 +118,14 @@ describe Homebrew::Livecheck do
     end
   end
 
+  let(:f_gist) do
+    formula("test_gist") do
+      desc "Gist test formula"
+      homepage "https://brew.sh"
+      url "https://gist.github.com/Homebrew/0000000000"
+    end
+  end
+
   let(:f_skip) do
     formula("test_skip") do
       desc "Skipped test formula"
@@ -66,31 +138,6 @@ describe Homebrew::Livecheck do
     end
   end
 
-  let(:f_versioned) do
-    formula("test@0.0.1") do
-      desc "Versioned test formula"
-      homepage "https://brew.sh"
-      url "https://brew.sh/test-0.0.1.tgz"
-    end
-  end
-
-  let(:c) do
-    Cask::CaskLoader.load(+<<-RUBY)
-      cask "test" do
-        version "0.0.1,2"
-
-        url "https://brew.sh/test-0.0.1.tgz"
-        name "Test"
-        homepage "https://brew.sh"
-
-        livecheck do
-          url "https://formulae.brew.sh/api/formula/ruby.json"
-          regex(/"stable":"(\d+(?:\.\d+)+)"/i)
-        end
-      end
-    RUBY
-  end
-
   describe "::formula_name" do
     it "returns the name of the formula" do
       expect(livecheck.formula_name(f)).to eq("test")
@@ -132,6 +179,12 @@ describe Homebrew::Livecheck do
         .and not_to_output.to_stderr
     end
 
+    it "skips a discontinued cask without a livecheckable" do
+      expect { livecheck.skip_conditions(c_discontinued) }
+        .to output("test_discontinued : discontinued\n").to_stdout
+        .and not_to_output.to_stderr
+    end
+
     it "skips a disabled formula without a livecheckable" do
       expect { livecheck.skip_conditions(f_disabled) }
         .to output("test_disabled : disabled\n").to_stdout
@@ -144,6 +197,18 @@ describe Homebrew::Livecheck do
         .and not_to_output.to_stderr
     end
 
+    it "skips a cask containing `version :latest` without a livecheckable" do
+      expect { livecheck.skip_conditions(c_latest) }
+        .to output("test_latest : latest\n").to_stdout
+        .and not_to_output.to_stderr
+    end
+
+    it "skips a cask containing an unversioned URL without a livecheckable" do
+      expect { livecheck.skip_conditions(c_unversioned) }
+        .to output("test_unversioned : unversioned\n").to_stdout
+        .and not_to_output.to_stderr
+    end
+
     it "skips a HEAD-only formula if not installed" do
       expect { livecheck.skip_conditions(f_head_only) }
         .to output("test_head_only : HEAD only formula must be installed to be livecheckable\n").to_stdout
diff --git a/Library/Homebrew/test/livecheck/strategy/header_match_spec.rb b/Library/Homebrew/test/livecheck/strategy/header_match_spec.rb
new file mode 100644
index 0000000000..fbb38b8366
--- /dev/null
+++ b/Library/Homebrew/test/livecheck/strategy/header_match_spec.rb
@@ -0,0 +1,16 @@
+# typed: false
+# frozen_string_literal: true
+
+require "livecheck/strategy/header_match"
+
+describe Homebrew::Livecheck::Strategy::HeaderMatch do
+  subject(:header_match) { described_class }
+
+  let(:url) { "https://www.example.com/" }
+
+  describe "::match?" do
+    it "returns true for any URL" do
+      expect(header_match.match?(url)).to be true
+    end
+  end
+end
diff --git a/Library/Homebrew/test/livecheck/strategy/sparkle_spec.rb b/Library/Homebrew/test/livecheck/strategy/sparkle_spec.rb
new file mode 100644
index 0000000000..f98e43ef00
--- /dev/null
+++ b/Library/Homebrew/test/livecheck/strategy/sparkle_spec.rb
@@ -0,0 +1,74 @@
+# typed: false
+# frozen_string_literal: true
+
+require "livecheck/strategy/sparkle"
+
+describe Homebrew::Livecheck::Strategy::Sparkle do
+  subject(:sparkle) { described_class }
+
+  let(:url) { "https://www.example.com/example/appcast.xml" }
+
+  let(:appcast_data) {
+    {
+      title:          "Version 1.2.3",
+      url:            "https://www.example.com/example/example.tar.gz",
+      bundle_version: Homebrew::BundleVersion.new("1.2.3", "1234"),
+      short_version:  "1.2.3",
+      version:        "1234",
+    }
+  }
+
+  let(:appcast_item) {
+    Homebrew::Livecheck::Strategy::Sparkle::Item.new(
+      {
+        title:          appcast_data[:title],
+        url:            appcast_data[:url],
+        bundle_version: appcast_data[:bundle_version],
+        short_version:  appcast_data[:bundle_version]&.short_version,
+        version:        appcast_data[:bundle_version]&.version,
+      },
+    )
+  }
+
+  let(:appcast_xml) {
+    <<~EOS
+      <?xml version="1.0" encoding="utf-8"?>
+      <rss version="2.0" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:sparkle="http://www.andymatuschak.org/xml-namespaces/sparkle">
+        <channel>
+          <title>Example Changelog</title>
+          <link>#{url}</link>
+          <description>Most recent changes with links to updates.</description>
+          <language>en</language>
+          <item>
+            <title>#{appcast_data[:title]}</title>
+            <sparkle:minimumSystemVersion>10.10</sparkle:minimumSystemVersion>
+            <sparkle:releaseNotesLink>https://www.example.com/example/1.2.3.html</sparkle:releaseNotesLink>
+            <enclosure url="#{appcast_data[:url]}" sparkle:shortVersionString="#{appcast_data[:short_version]}" sparkle:version="#{appcast_data[:version]}" length="12345678" type="application/octet-stream" sparkle:dsaSignature="ABCDEF+GHIJKLMNOPQRSTUVWXYZab/cdefghijklmnopqrst/uvwxyz1234567==" />
+          </item>
+        </channel>
+      </rss>
+    EOS
+  }
+
+  describe "::match?" do
+    it "returns true for any URL" do
+      expect(sparkle.match?(url)).to be true
+    end
+  end
+
+  describe "::item_from_content" do
+    let(:item_from_appcast_xml) { sparkle.item_from_content(appcast_xml) }
+
+    it "returns nil if content is blank" do
+      expect(sparkle.item_from_content("")).to be nil
+    end
+
+    it "returns an Item when given XML data" do
+      expect(item_from_appcast_xml).to be_a(Homebrew::Livecheck::Strategy::Sparkle::Item)
+      expect(item_from_appcast_xml.title).to eq(appcast_item.title)
+      expect(item_from_appcast_xml.url).to eq(appcast_item.url)
+      expect(item_from_appcast_xml.bundle_version.short_version).to eq(appcast_item.bundle_version.short_version)
+      expect(item_from_appcast_xml.bundle_version.version).to eq(appcast_item.bundle_version.version)
+    end
+  end
+end
diff --git a/Library/Homebrew/version.rb b/Library/Homebrew/version.rb
index 8c1735e9a1..c3c86456ac 100644
--- a/Library/Homebrew/version.rb
+++ b/Library/Homebrew/version.rb
@@ -318,11 +318,13 @@ class Version
   end
 
   def self.parse(spec, detected_from_url: false)
-    version = _parse(spec)
+    version = _parse(spec, detected_from_url: detected_from_url)
     version.nil? ? NULL : new(version, detected_from_url: detected_from_url)
   end
 
-  def self._parse(spec)
+  def self._parse(spec, detected_from_url:)
+    spec = CGI.unescape(spec.to_s) if detected_from_url
+
     spec = Pathname.new(spec) unless spec.is_a? Pathname
 
     spec_s = spec.to_s
@@ -465,7 +467,6 @@ class Version
     m = /[-.vV]?((?:\d+\.)+\d+(?:[-_.]?(?i:alpha|beta|pre|rc)\.?\d{,2})?)/.match(spec_s)
     return m.captures.first unless m.nil?
   end
-
   private_class_method :_parse
 
   def initialize(val, detected_from_url: false)