diff --git a/Library/Homebrew/cmd/reinstall.rb b/Library/Homebrew/cmd/reinstall.rb
index fac1a3096d..8f73846cb0 100644
--- a/Library/Homebrew/cmd/reinstall.rb
+++ b/Library/Homebrew/cmd/reinstall.rb
@@ -7,6 +7,7 @@
 require "formula_installer"
 require "development_tools"
 require "messages"
+require "reinstall"
 
 module Homebrew
   module_function
@@ -26,59 +27,4 @@ module Homebrew
     end
     Homebrew.messages.display_messages
   end
-
-  def reinstall_formula(f)
-    if f.opt_prefix.directory?
-      keg = Keg.new(f.opt_prefix.resolved_path)
-      keg_had_linked_opt = true
-      keg_was_linked = keg.linked?
-      backup keg
-    end
-
-    build_options = BuildOptions.new(Options.create(ARGV.flags_only), f.options)
-    options = build_options.used_options
-    options |= f.build.used_options
-    options &= f.options
-
-    fi = FormulaInstaller.new(f)
-    fi.options              = options
-    fi.invalid_option_names = build_options.invalid_option_names
-    fi.build_bottle         = ARGV.build_bottle? || (!f.bottled? && f.build.bottle?)
-    fi.interactive          = ARGV.interactive?
-    fi.git                  = ARGV.git?
-    fi.link_keg           ||= keg_was_linked if keg_had_linked_opt
-    fi.prelude
-
-    oh1 "Reinstalling #{Formatter.identifier(f.full_name)} #{options.to_a.join " "}"
-
-    fi.install
-    fi.finish
-  rescue FormulaInstallationAlreadyAttemptedError
-    nil
-  rescue Exception # rubocop:disable Lint/RescueException
-    ignore_interrupts { restore_backup(keg, keg_was_linked) }
-    raise
-  else
-    backup_path(keg).rmtree if backup_path(keg).exist?
-  end
-
-  def backup(keg)
-    keg.unlink
-    keg.rename backup_path(keg)
-  end
-
-  def restore_backup(keg, keg_was_linked)
-    path = backup_path(keg)
-
-    return unless path.directory?
-
-    Pathname.new(keg).rmtree if keg.exist?
-
-    path.rename keg
-    keg.link if keg_was_linked
-  end
-
-  def backup_path(path)
-    Pathname.new "#{path}.reinstall"
-  end
 end
diff --git a/Library/Homebrew/cmd/upgrade.rb b/Library/Homebrew/cmd/upgrade.rb
index f170d1f220..858ca47e10 100644
--- a/Library/Homebrew/cmd/upgrade.rb
+++ b/Library/Homebrew/cmd/upgrade.rb
@@ -21,6 +21,7 @@
 #:    are pinned; see `pin`, `unpin`).
 
 require "install"
+require "reinstall"
 require "formula_installer"
 require "cleanup"
 require "development_tools"
@@ -80,6 +81,16 @@ module Homebrew
       puts formulae_upgrades.join(", ")
     end
 
+    upgrade_formulae(formulae_to_install)
+
+    check_dependents(formulae_to_install)
+
+    Homebrew.messages.display_messages
+  end
+
+  def upgrade_formulae(formulae_to_install)
+    return if formulae_to_install.empty?
+
     # Sort keg_only before non-keg_only formulae to avoid any needless conflicts
     # with outdated, non-keg_only versions of formulae being upgraded.
     formulae_to_install.sort! do |a, b|
@@ -104,7 +115,6 @@ module Homebrew
         onoe "#{f}: #{e}"
       end
     end
-    Homebrew.messages.display_messages
   end
 
   def upgrade_formula(f)
@@ -171,4 +181,189 @@ module Homebrew
       nil
     end
   end
+
+  def upgradable_dependents(kegs, formulae)
+    formulae_to_upgrade = Set.new
+    formulae_pinned = Set.new
+
+    formulae.each do |formula|
+      descendants = Set.new
+
+      dependents = kegs.select do |keg|
+        keg.runtime_dependencies
+           .any? { |d| d["full_name"] == formula.full_name }
+      end
+
+      next if dependents.empty?
+
+      dependent_formulae = dependents.map(&:to_formula)
+
+      dependent_formulae.each do |f|
+        next if formulae_to_upgrade.include?(f)
+        next if formulae_pinned.include?(f)
+
+        if f.outdated?(fetch_head: ARGV.fetch_head?)
+          if f.pinned?
+            formulae_pinned << f
+          else
+            formulae_to_upgrade << f
+          end
+        end
+
+        descendants << f
+      end
+
+      upgradable_descendants, pinned_descendants = upgradable_dependents(kegs, descendants)
+
+      formulae_to_upgrade.merge upgradable_descendants
+      formulae_pinned.merge pinned_descendants
+    end
+
+    [formulae_to_upgrade, formulae_pinned]
+  end
+
+  def broken_dependents(kegs, formulae)
+    formulae_to_reinstall = Set.new
+    formulae_pinned_and_outdated = Set.new
+
+    CacheStoreDatabase.use(:linkage) do |db|
+      formulae.each do |formula|
+        descendants = Set.new
+
+        dependents = kegs.select do |keg|
+          keg.runtime_dependencies
+             .any? { |d| d["full_name"] == formula.full_name }
+        end
+
+        next if dependents.empty?
+
+        dependents.each do |keg|
+          f = keg.to_formula
+
+          next if formulae_to_reinstall.include?(f)
+          next if formulae_pinned_and_outdated.include?(f)
+
+          checker = LinkageChecker.new(keg, cache_db: db)
+
+          if checker.broken_library_linkage?
+            if f.outdated?(fetch_head: ARGV.fetch_head?)
+              # Outdated formulae = pinned formulae (see function above)
+              formulae_pinned_and_outdated << f
+            else
+              formulae_to_reinstall << f
+            end
+          end
+
+          descendants << f
+        end
+
+        descendants_to_reinstall, descendants_pinned = broken_dependents(kegs, descendants)
+
+        formulae_to_reinstall.merge descendants_to_reinstall
+        formulae_pinned_and_outdated.merge descendants_pinned
+      end
+    end
+
+    [formulae_to_reinstall, formulae_pinned_and_outdated]
+  end
+
+  # @private
+  def depends_on(a, b)
+    if a.opt_or_installed_prefix_keg
+        .runtime_dependencies
+        .any? { |d| d["full_name"] == b.full_name }
+      1
+    else
+      a <=> b
+    end
+  end
+
+  # @private
+  def formulae_with_runtime_dependencies
+    Formula.installed
+           .map(&:opt_or_installed_prefix_keg)
+           .reject(&:nil?)
+           .reject { |f| f.runtime_dependencies.to_a.empty? }
+  end
+
+  def check_dependents(formulae)
+    return if formulae.empty?
+
+    # First find all the outdated dependents.
+    kegs = formulae_with_runtime_dependencies
+
+    return if kegs.empty?
+
+    oh1 "Checking dependents for outdated formulae" if ARGV.verbose?
+    upgradable, pinned = upgradable_dependents(kegs, formulae).map(&:to_a)
+
+    upgradable.sort! { |a, b| depends_on(a, b) }
+
+    pinned.sort! { |a, b| depends_on(a, b) }
+
+    # Print the pinned dependents.
+    unless pinned.empty?
+      ohai "Not upgrading #{Formatter.pluralize(pinned.length, "pinned dependent")}:"
+      puts pinned.map { |f| "#{f.full_specified_name} #{f.pkg_version}" } * ", "
+    end
+
+    # Print the upgradable dependents.
+    if upgradable.empty?
+      ohai "No dependents to upgrade" if ARGV.verbose?
+    else
+      ohai "Upgrading #{Formatter.pluralize(upgradable.length, "dependent")}:"
+      formulae_upgrades = upgradable.map do |f|
+        if f.optlinked?
+          "#{f.full_specified_name} #{Keg.new(f.opt_prefix).version} -> #{f.pkg_version}"
+        else
+          "#{f.full_specified_name} #{f.pkg_version}"
+        end
+      end
+      puts formulae_upgrades.join(", ")
+    end
+
+    upgrade_formulae(upgradable)
+
+    # Assess the dependents tree again.
+    kegs = formulae_with_runtime_dependencies
+
+    oh1 "Checking dependents for broken library links" if ARGV.verbose?
+    reinstallable, pinned = broken_dependents(kegs, formulae).map(&:to_a)
+
+    reinstallable.sort! { |a, b| depends_on(a, b) }
+
+    pinned.sort! { |a, b| depends_on(a, b) }
+
+    # Print the pinned dependents.
+    unless pinned.empty?
+      onoe "Not reinstalling #{Formatter.pluralize(pinned.length, "broken and outdated, but pinned dependent")}:"
+      $stderr.puts pinned.map { |f| "#{f.full_specified_name} #{f.pkg_version}" } * ", "
+    end
+
+    # Print the broken dependents.
+    if reinstallable.empty?
+      ohai "No broken dependents to reinstall" if ARGV.verbose?
+    else
+      ohai "Reinstalling #{Formatter.pluralize(reinstallable.length, "broken dependent")} from source:"
+      puts reinstallable.map(&:full_specified_name).join(", ")
+    end
+
+    reinstallable.each do |f|
+      begin
+        reinstall_formula(f, build_from_source: true)
+      rescue FormulaInstallationAlreadyAttemptedError
+        # We already attempted to reinstall f as part of the dependency tree of
+        # another formula. In that case, don't generate an error, just move on.
+        nil
+      rescue CannotInstallFormulaError => e
+        ofail e
+      rescue BuildError => e
+        e.dump
+        puts
+        Homebrew.failed = true
+      rescue DownloadError => e
+        ofail e
+      end
+    end
+  end
 end
diff --git a/Library/Homebrew/reinstall.rb b/Library/Homebrew/reinstall.rb
new file mode 100644
index 0000000000..33f7c37b6a
--- /dev/null
+++ b/Library/Homebrew/reinstall.rb
@@ -0,0 +1,63 @@
+require "formula_installer"
+require "development_tools"
+require "messages"
+
+module Homebrew
+  module_function
+
+  def reinstall_formula(f, build_from_source: false)
+    if f.opt_prefix.directory?
+      keg = Keg.new(f.opt_prefix.resolved_path)
+      keg_had_linked_opt = true
+      keg_was_linked = keg.linked?
+      backup keg
+    end
+
+    build_options = BuildOptions.new(Options.create(ARGV.flags_only), f.options)
+    options = build_options.used_options
+    options |= f.build.used_options
+    options &= f.options
+
+    fi = FormulaInstaller.new(f)
+    fi.options              = options
+    fi.invalid_option_names = build_options.invalid_option_names
+    fi.build_bottle         = ARGV.build_bottle? || (!f.bottled? && f.build.bottle?)
+    fi.interactive          = ARGV.interactive?
+    fi.git                  = ARGV.git?
+    fi.link_keg           ||= keg_was_linked if keg_had_linked_opt
+    fi.build_from_source    = true if build_from_source
+    fi.prelude
+
+    oh1 "Reinstalling #{Formatter.identifier(f.full_name)} #{options.to_a.join " "}"
+
+    fi.install
+    fi.finish
+  rescue FormulaInstallationAlreadyAttemptedError
+    nil
+  rescue Exception # rubocop:disable Lint/RescueException
+    ignore_interrupts { restore_backup(keg, keg_was_linked) }
+    raise
+  else
+    backup_path(keg).rmtree if backup_path(keg).exist?
+  end
+
+  def backup(keg)
+    keg.unlink
+    keg.rename backup_path(keg)
+  end
+
+  def restore_backup(keg, keg_was_linked)
+    path = backup_path(keg)
+
+    return unless path.directory?
+
+    Pathname.new(keg).rmtree if keg.exist?
+
+    path.rename keg
+    keg.link if keg_was_linked
+  end
+
+  def backup_path(path)
+    Pathname.new "#{path}.reinstall"
+  end
+end
diff --git a/Library/Homebrew/test/cmd/upgrade_spec.rb b/Library/Homebrew/test/cmd/upgrade_spec.rb
index 10d5386a11..cb6934d4c3 100644
--- a/Library/Homebrew/test/cmd/upgrade_spec.rb
+++ b/Library/Homebrew/test/cmd/upgrade_spec.rb
@@ -7,4 +7,14 @@ describe "brew upgrade", :integration_test do
 
     expect(HOMEBREW_CELLAR/"testball/0.1").to be_a_directory
   end
+
+  it "upgrades a Formula and cleans up old versions" do
+    setup_test_formula "testball"
+    (HOMEBREW_CELLAR/"testball/0.0.1/foo").mkpath
+
+    expect { brew "upgrade", "--cleanup" }.to be_a_success
+
+    expect(HOMEBREW_CELLAR/"testball/0.1").to be_a_directory
+    expect(HOMEBREW_CELLAR/"testball/0.0.1").not_to exist
+  end
 end