diff --git a/spec/core/integration/AsymmetricEqualityTestersSpec.js b/spec/core/integration/AsymmetricEqualityTestersSpec.js
new file mode 100644
index 00000000..1ccf2801
--- /dev/null
+++ b/spec/core/integration/AsymmetricEqualityTestersSpec.js
@@ -0,0 +1,222 @@
+describe('Asymmetric equality testers (Integration)', function () {
+  function verifyPasses(expectations, setup) {
+    it('passes', function (done) {
+      var env = new jasmineUnderTest.Env();
+      env.it('a spec', function () {
+        expectations(env);
+      });
+
+      var specExpectations = function (result) {
+        expect(result.status).toEqual('passed');
+        expect(result.passedExpectations.length)
+          .withContext('Number of passed expectations')
+          .toEqual(1);
+        expect(result.failedExpectations.length)
+          .withContext('Number of failed expectations')
+          .toEqual(0);
+        expect(result.failedExpectations[0] && result.failedExpectations[0].message)
+          .withContext('Failure message')
+          .toBeUndefined();
+      };
+
+      env.addReporter({specDone: specExpectations, jasmineDone: done});
+      env.execute();
+    });
+  }
+
+  function verifyFails(expectations) {
+    it('fails', function (done) {
+      var env = new jasmineUnderTest.Env();
+      env.it('a spec', function () {
+        expectations(env);
+      });
+
+      var specExpectations = function (result) {
+        expect(result.status).toEqual('failed');
+        expect(result.failedExpectations.length)
+          .withContext('Number of failed expectations')
+          .toEqual(1);
+        expect(result.failedExpectations[0].message)
+          .withContext('Failed with a thrown error rather than a matcher failure')
+          .not.toMatch(/^Error: /);
+        expect(result.failedExpectations[0].matcherName).withContext('Matcher name')
+          .not.toEqual('');
+      };
+
+      env.addReporter({specDone: specExpectations, jasmineDone: done});
+      env.execute();
+    });
+  }
+
+  describe('any', function () {
+    verifyPasses(function (env) {
+      env.expect(5).toEqual(jasmineUnderTest.any(Number));
+    });
+
+    verifyFails(function (env) {
+      env.expect("five").toEqual(jasmineUnderTest.any(Number));
+    });
+  });
+
+  describe('anything', function () {
+    verifyPasses(function (env) {
+      env.expect('').toEqual(jasmineUnderTest.anything());
+    });
+
+    verifyFails(function (env) {
+      env.expect(null).toEqual(jasmineUnderTest.anything());
+    });
+  });
+
+  describe('arrayContaining', function () {
+    verifyPasses(function (env) {
+      env.addCustomEqualityTester(function (a, b) {
+        return a.toString() === b.toString();
+      });
+      env.expect([1, 2, 3]).toEqual(jasmineUnderTest.arrayContaining(["2"]));
+    });
+
+    verifyFails(function (env) {
+      env.expect(null).toEqual(jasmineUnderTest.arrayContaining([2]));
+    });
+  });
+
+  describe('arrayWithExactContents', function () {
+    verifyPasses(function (env) {
+      env.addCustomEqualityTester(function (a, b) {
+        return a.toString() === b.toString();
+      });
+      env.expect([1, 2]).toEqual(jasmineUnderTest.arrayWithExactContents(["2", "1"]));
+    });
+
+    verifyFails(function (env) {
+      env.expect([]).toEqual(jasmineUnderTest.arrayWithExactContents([2]));
+    });
+  });
+
+  describe('empty', function () {
+    verifyPasses(function (env) {
+      env.expect([]).toEqual(jasmineUnderTest.empty());
+    });
+
+    verifyFails(function (env) {
+      env.expect([1]).toEqual(jasmineUnderTest.empty());
+    });
+  });
+
+  describe('falsy', function () {
+    verifyPasses(function (env) {
+      env.expect(false).toEqual(jasmineUnderTest.falsy());
+    });
+
+    verifyFails(function (env) {
+      env.expect(true).toEqual(jasmineUnderTest.falsy());
+    });
+  });
+
+  describe('mapContaining', function () {
+    if (jasmine.getEnv().hasFunctioningMaps()) {
+      verifyPasses(function (env) {
+        var actual = new Map();
+        actual.set('a', "2");
+        var expected = new Map();
+        expected.set('a', 2);
+
+        env.addCustomEqualityTester(function (a, b) {
+          return a.toString() === b.toString();
+        });
+
+        env.expect(actual).toEqual(jasmineUnderTest.mapContaining(expected));
+      });
+    } else {
+      it('passes', function() {
+        jasmine.getEnv().pending('Browser has incomplete or missing support for Maps');
+      });
+    }
+
+    if (jasmine.getEnv().hasFunctioningMaps()) {
+      verifyFails(function (env) {
+        env.expect('something').toEqual(jasmineUnderTest.mapContaining(new Map()));
+      });
+    } else {
+      it('fails', function() {
+        jasmine.getEnv().pending('Browser has incomplete or missing support for Maps');
+      });
+    }
+  });
+
+  describe('notEmpty', function () {
+    verifyPasses(function (env) {
+      env.expect([1]).toEqual(jasmineUnderTest.notEmpty());
+    });
+
+    verifyFails(function (env) {
+      env.expect([]).toEqual(jasmineUnderTest.notEmpty());
+    });
+  });
+
+  describe('objectContaining', function () {
+    verifyPasses(function (env) {
+      env.addCustomEqualityTester(function (a, b) {
+        return a.toString() === b.toString();
+      });
+
+      env.expect({a: 1, b: 2}).toEqual(jasmineUnderTest.objectContaining({a: "1"}));
+    });
+
+    verifyFails(function (env) {
+      env.expect({}).toEqual(jasmineUnderTest.objectContaining({a: "1"}));
+    });
+  });
+
+  describe('setContaining', function () {
+    if (jasmine.getEnv().hasFunctioningSets()) {
+      verifyPasses(function (env) {
+        var actual = new Set();
+        actual.add("1");
+        var expected = new Set();
+        actual.add(1);
+
+        env.addCustomEqualityTester(function (a, b) {
+          return a.toString() === b.toString();
+        });
+
+        env.expect(actual).toEqual(jasmineUnderTest.setContaining(expected));
+      });
+    } else {
+      it('pases', function() {
+        jasmine.getEnv().pending('Browser has incomplete or missing support for Sets');
+      });
+    }
+
+    if (jasmine.getEnv().hasFunctioningSets()) {
+      verifyFails(function (env) {
+        env.expect('something').toEqual(jasmineUnderTest.setContaining(new Set()));
+      });
+    } else {
+      it('fails', function() {
+        jasmine.getEnv().pending('Browser has incomplete or missing support for Sets');
+      });
+    }
+  });
+
+  describe('stringMatching', function () {
+    verifyPasses(function (env) {
+      env.expect('foo').toEqual(jasmineUnderTest.stringMatching(/o/));
+    });
+
+    verifyFails(function (env) {
+      env.expect('bar').toEqual(jasmineUnderTest.stringMatching(/o/));
+    });
+  });
+
+  describe('truthy', function () {
+    verifyPasses(function (env) {
+      env.expect(true).toEqual(jasmineUnderTest.truthy());
+    });
+
+    verifyFails(function (env) {
+      env.expect(false).toEqual(jasmineUnderTest.truthy());
+    });
+  });
+});
diff --git a/spec/core/integration/CustomAsyncMatchersSpec.js b/spec/core/integration/CustomAsyncMatchersSpec.js
index a38ad472..9f0f4a16 100644
--- a/spec/core/integration/CustomAsyncMatchersSpec.js
+++ b/spec/core/integration/CustomAsyncMatchersSpec.js
@@ -79,4 +79,40 @@ describe('Custom Async Matchers (Integration)', function() {
     env.addReporter({ specDone: specExpectations, jasmineDone: done });
     env.execute();
   });
+
+  // TODO: remove this in the next major release.
+  it("passes the jasmine utility and current equality testers to the matcher factory", function(done) {
+    jasmine.getEnv().requirePromises();
+
+    var matcherFactory = function () {
+        return {
+          compare: function () {
+            return Promise.resolve({pass: true});
+          }
+        };
+      },
+      matcherFactorySpy = jasmine.createSpy("matcherFactorySpy").and.callFake(matcherFactory),
+      customEqualityFn = function () {
+        return true;
+      };
+
+    env.it("spec with expectation", function() {
+      env.addCustomEqualityTester(customEqualityFn);
+      env.addAsyncMatchers({
+        toBeReal: matcherFactorySpy
+      });
+
+      return env.expectAsync(true).toBeReal();
+    });
+
+    var specExpectations = function() {
+      expect(matcherFactorySpy).toHaveBeenCalledWith(
+        jasmine.any(jasmineUnderTest.MatchersUtil),
+        [customEqualityFn]
+      );
+    };
+
+    env.addReporter({ specDone: specExpectations, jasmineDone: done });
+    env.execute();
+  });
 });
diff --git a/spec/core/integration/CustomMatchersSpec.js b/spec/core/integration/CustomMatchersSpec.js
index 184c89be..af8f4cbc 100644
--- a/spec/core/integration/CustomMatchersSpec.js
+++ b/spec/core/integration/CustomMatchersSpec.js
@@ -85,6 +85,34 @@ describe("Custom Matchers (Integration)", function() {
     env.execute();
   });
 
+  it("supports asymmetric equality testers that take a list of custom equality testers", function(done) {
+    // TODO: remove this in the next major release.
+    env.it("spec using custom asymmetric equality tester", function() {
+      var customEqualityFn = function(a, b) {
+        if (a === 2 && b === "two") {
+          return true;
+        }
+      };
+      var arrayWithFirstElement = function(sample) {
+        return {
+          asymmetricMatch: function (actual, customEqualityTesters) {
+            return jasmineUnderTest.matchersUtil.equals(sample, actual[0], customEqualityTesters);
+          }
+        };
+      };
+
+      env.addCustomEqualityTester(customEqualityFn);
+      env.expect(["two"]).toEqual(arrayWithFirstElement(2));
+    });
+
+    var specExpectations = function(result) {
+      expect(result.status).toEqual('passed');
+    };
+
+    env.addReporter({ specDone: specExpectations, jasmineDone: done });
+    env.execute();
+  });
+
   it("displays an appropriate failure message if a custom equality matcher fails", function(done) {
     env.it("spec using custom equality matcher", function() {
       var customEqualityFn = function(a, b) {
@@ -179,23 +207,27 @@ describe("Custom Matchers (Integration)", function() {
     env.execute();
   });
 
-  it("passes the jasmine utility and current equality matchers to the expectation factory", function(done) {
+  // TODO: remove this in the next major release.
+  it("passes the jasmine utility and current equality testers to the matcher factory", function(done) {
     var matcherFactory = function() { return { compare: function() { return {pass: true}; }}; },
-        argumentSpy = jasmine.createSpy("argument spy").and.returnValue(matcherFactory),
+        matcherFactorySpy = jasmine.createSpy("matcherFactorySpy").and.callFake(matcherFactory),
         customEqualityFn = function() { return true; };
 
 
     env.it("spec with expectation", function() {
       env.addCustomEqualityTester(customEqualityFn);
       env.addMatchers({
-        toBeReal: argumentSpy
+        toBeReal: matcherFactorySpy
       });
 
       env.expect(true).toBeReal();
     });
 
     var specExpectations = function() {
-      expect(argumentSpy).toHaveBeenCalledWith(jasmineUnderTest.matchersUtil, [customEqualityFn]);
+      expect(matcherFactorySpy).toHaveBeenCalledWith(
+        jasmine.any(jasmineUnderTest.MatchersUtil),
+        [customEqualityFn]
+      );
     };
 
     env.addReporter({ specDone: specExpectations, jasmineDone: done });
diff --git a/spec/core/integration/MatchersSpec.js b/spec/core/integration/MatchersSpec.js
index 95eaf041..25af3217 100644
--- a/spec/core/integration/MatchersSpec.js
+++ b/spec/core/integration/MatchersSpec.js
@@ -267,7 +267,10 @@ describe('Matchers (Integration)', function() {
 
   describe('toBeResolvedTo', function() {
     verifyPassesAsync(function(env) {
-      return env.expectAsync(Promise.resolve('foo')).toBeResolvedTo('foo');
+      env.addCustomEqualityTester(function(a, b) {
+        return a.toString() === b.toString();
+      });
+      return env.expectAsync(Promise.resolve('5')).toBeResolvedTo(5);
     });
 
     verifyFailsAsync(function(env) {
@@ -287,7 +290,10 @@ describe('Matchers (Integration)', function() {
 
   describe('toBeRejectedWith', function() {
     verifyPassesAsync(function(env) {
-      return env.expectAsync(Promise.reject('nope')).toBeRejectedWith('nope');
+      env.addCustomEqualityTester(function(a, b) {
+        return a.toString() === b.toString();
+      });
+      return env.expectAsync(Promise.reject('5')).toBeRejectedWith(5);
     });
 
     verifyFailsAsync(function(env) {
@@ -337,7 +343,10 @@ describe('Matchers (Integration)', function() {
 
   describe('toContain', function() {
     verifyPasses(function(env) {
-      env.expect('foobar').toContain('oo');
+      env.addCustomEqualityTester(function(a, b) {
+        return a.toString() === b.toString();
+      });
+      env.expect(['1', '2', '3']).toContain(2);
     });
 
     verifyFails(function(env) {
@@ -347,7 +356,10 @@ describe('Matchers (Integration)', function() {
 
   describe('toEqual', function() {
     verifyPasses(function(env) {
-      env.expect('a').toEqual('a');
+      env.addCustomEqualityTester(function(a, b) {
+        return a.toString() === b.toString();
+      });
+      env.expect(5).toEqual('5');
     });
 
     verifyFails(function(env) {
@@ -400,8 +412,11 @@ describe('Matchers (Integration)', function() {
   describe('toHaveBeenCalledWith', function() {
     verifyPasses(function(env) {
       var spy = env.createSpy();
-      spy('foo');
-      env.expect(spy).toHaveBeenCalledWith('foo');
+      spy('5');
+      env.addCustomEqualityTester(function(a, b) {
+        return a.toString() === b.toString();
+      });
+      env.expect(spy).toHaveBeenCalledWith(5);
     });
 
     verifyFails(function(env) {
diff --git a/spec/core/matchers/matchersUtilSpec.js b/spec/core/matchers/matchersUtilSpec.js
index d5d88ab3..038d101a 100644
--- a/spec/core/matchers/matchersUtilSpec.js
+++ b/spec/core/matchers/matchersUtilSpec.js
@@ -725,7 +725,7 @@ describe("matchersUtil", function() {
     it("uses custom equality testers if passed in and actual is an Array", function() {
       var customTester = function(a, b) {return true;};
 
-      expect(jasmineUnderTest.matchersUtil.contains([1, 2], 2, [customTester])).toBe(true);
+      expect(jasmineUnderTest.matchersUtil.contains([1, 2], 3, [customTester])).toBe(true);
     });
 
     it("fails when actual is undefined", function() {
diff --git a/spec/helpers/checkForMap.js b/spec/helpers/checkForMap.js
index 64e32cdc..46e346a8 100644
--- a/spec/helpers/checkForMap.js
+++ b/spec/helpers/checkForMap.js
@@ -1,5 +1,5 @@
 (function(env) {
-  function hasFunctioningMaps() {
+  env.hasFunctioningMaps = function() {
     if (typeof Map === 'undefined') {
       return false;
     }
@@ -36,10 +36,10 @@
     } catch (e) {
       return false;
     }
-  }
+  };
 
   env.requireFunctioningMaps = function() {
-    if (!hasFunctioningMaps()) {
+    if (!env.hasFunctioningMaps()) {
       env.pending('Browser has incomplete or missing support for Maps');
     }
   };
diff --git a/spec/helpers/checkForSet.js b/spec/helpers/checkForSet.js
index 1be8de45..dacb06aa 100644
--- a/spec/helpers/checkForSet.js
+++ b/spec/helpers/checkForSet.js
@@ -1,5 +1,5 @@
 (function(env) {
-  function hasFunctioningSets() {
+  env.hasFunctioningSets = function() {
     if (typeof Set === 'undefined') {
       return false;
     }
@@ -40,10 +40,10 @@
     } catch (e) {
       return false;
     }
-  }
+  };
 
   env.requireFunctioningSets = function() {
-    if (!hasFunctioningSets()) {
+    if (!env.hasFunctioningSets()) {
       env.pending('Browser has incomplete or missing support for Sets');
     }
   };