diff --git a/spec/core/asymmetric_equality/MapContainingSpec.js b/spec/core/asymmetric_equality/MapContainingSpec.js
new file mode 100644
index 00000000..a214dce8
--- /dev/null
+++ b/spec/core/asymmetric_equality/MapContainingSpec.js
@@ -0,0 +1,183 @@
+describe('MapContaining', function() {
+  function MapI(iterable) {    // for IE11
+    var map = new Map();
+    iterable.forEach(function(kv) {
+      map.set(kv[0], kv[1]);
+    });
+    return map;
+  }
+
+  beforeEach(function() {
+    jasmine.getEnv().requireFunctioningMaps();
+  });
+
+
+  it('matches any actual map to an empty map', function() {
+    var actualMap = new MapI([['foo', 'bar']]);
+    var containing = new jasmineUnderTest.MapContaining(new Map());
+
+    expect(containing.asymmetricMatch(actualMap)).toBe(true);
+  });
+
+  it('matches when all the key/value pairs in sample have matches in actual', function() {
+    var actualMap = new MapI([
+      ['foo', [1, 2, 3]],
+      [{'foo': 'bar'}, 'baz'],
+      ['other', 'any'],
+    ]);
+
+    var containingMap = new MapI([
+      [{'foo': 'bar'}, 'baz'],
+      ['foo', [1, 2, 3]],
+    ]);
+    var containing = new jasmineUnderTest.MapContaining(containingMap);
+
+    expect(containing.asymmetricMatch(actualMap)).toBe(true);
+  });
+
+  it('does not match when a key is not in actual', function() {
+    var actualMap = new MapI([
+      ['foo', [1, 2, 3]],
+      [{'foo': 'not a bar'}, 'baz'],
+    ]);
+
+    var containingMap = new MapI([
+      [{'foo': 'bar'}, 'baz'],
+      ['foo', [1, 2, 3]],
+    ]);
+    var containing = new jasmineUnderTest.MapContaining(containingMap);
+
+    expect(containing.asymmetricMatch(actualMap)).toBe(false);
+  });
+
+  it('does not match when a value is not in actual', function() {
+    var actualMap = new MapI([
+      ['foo', [1, 2, 3]],
+      [{'foo': 'bar'}, 'baz'],
+    ]);
+
+    var containingMap = new MapI([
+      [{'foo': 'bar'}, 'baz'],
+      ['foo', [1, 2]],
+    ]);
+    var containing = new jasmineUnderTest.MapContaining(containingMap);
+
+    expect(containing.asymmetricMatch(actualMap)).toBe(false);
+  });
+
+  it('matches when all the key/value pairs in sample have asymmetric matches in actual', function() {
+    var actualMap = new MapI([
+      ['foo1', 'not a bar'],
+      ['foo2', 'bar'],
+      ['baz', [1, 2, 3, 4]],
+    ]);
+
+    var containingMap = new MapI([
+      [
+        jasmine.stringMatching(/^foo\d/),
+        'bar'
+      ],
+      [
+        'baz',
+        jasmine.arrayContaining([2, 3])
+      ],
+    ]);
+    var containing = new jasmineUnderTest.MapContaining(containingMap);
+
+    expect(containing.asymmetricMatch(actualMap)).toBe(true);
+  });
+
+  it('does not match when a key in sample has no asymmetric matches in actual', function() {
+    var actualMap = new MapI([
+      ['a-foo1', 'bar'],
+      ['baz', [1, 2, 3, 4]],
+    ]);
+
+    var containingMap = new MapI([
+      [
+        jasmine.stringMatching(/^foo\d/),
+        'bar'
+      ],
+      [
+        'baz',
+        jasmine.arrayContaining([2, 3])
+      ],
+    ]);
+    var containing = new jasmineUnderTest.MapContaining(containingMap);
+
+    expect(containing.asymmetricMatch(actualMap)).toBe(false);
+  });
+
+  it('does not match when a value in sample has no asymmetric matches in actual', function() {
+    var actualMap = new MapI([
+      ['foo1', 'bar'],
+      ['baz', [1, 2, 3, 4]],
+    ]);
+
+    var containingMap = new MapI([
+      [
+        jasmine.stringMatching(/^foo\d/),
+        'bar'
+      ],
+      [
+        'baz',
+        jasmine.arrayContaining([4, 5])
+      ],
+    ]);
+    var containing = new jasmineUnderTest.MapContaining(containingMap);
+
+    expect(containing.asymmetricMatch(actualMap)).toBe(false);
+  });
+
+  it('matches recursively', function() {
+    var actualMap = new MapI([
+      ['foo', new MapI([['foo1', 1], ['foo2', 2]])],
+      [new MapI([[1, 'bar1'], [2, 'bar2']]), 'bar'],
+      ['other', 'any'],
+    ]);
+
+    var containingMap = new MapI([
+      [
+        'foo',
+        new jasmineUnderTest.MapContaining(new MapI([['foo1', 1]]))
+      ],
+      [
+        new jasmineUnderTest.MapContaining(new MapI([[2, 'bar2']])),
+        'bar'
+      ],
+    ]);
+    var containing = new jasmineUnderTest.MapContaining(containingMap);
+
+    expect(containing.asymmetricMatch(actualMap)).toBe(true);
+  });
+
+  it('uses custom equality testers', function() {
+    function tester(a, b) {
+      // treat all negative numbers as equal
+      return (typeof a == 'number' && typeof b == 'number') ? (a < 0 && b < 0) : a === b;
+    }
+    var actualMap = new MapI([['foo', -1]]);
+    var containing = new jasmineUnderTest.MapContaining(new MapI([['foo', -2]]));
+
+    expect(containing.asymmetricMatch(actualMap, [tester])).toBe(true);
+  });
+
+  it('does not match when actual is not a map', function() {
+    var containingMap = new MapI([['foo', 'bar']]);
+    expect(new jasmineUnderTest.MapContaining(containingMap).asymmetricMatch('foo')).toBe(false);
+    expect(new jasmineUnderTest.MapContaining(containingMap).asymmetricMatch(-1)).toBe(false);
+    expect(new jasmineUnderTest.MapContaining(containingMap).asymmetricMatch({'foo': 'bar'})).toBe(false);
+  });
+
+  it('throws an error when sample is not a map', function() {
+    expect(function() {
+      new jasmineUnderTest.MapContaining({'foo': 'bar'}).asymmetricMatch(new Map());
+    }).toThrowError(/You must provide a map/);
+  });
+
+  it('defines a `jasmineToString` method', function() {
+    var containing = new jasmineUnderTest.MapContaining(new Map());
+
+    expect(containing.jasmineToString()).toMatch(/^<jasmine\.mapContaining/);
+  });
+});
diff --git a/spec/core/asymmetric_equality/SetContainingSpec.js b/spec/core/asymmetric_equality/SetContainingSpec.js
new file mode 100644
index 00000000..d1ae7a5a
--- /dev/null
+++ b/spec/core/asymmetric_equality/SetContainingSpec.js
@@ -0,0 +1,118 @@
+describe('SetContaining', function() {
+  function SetI(iterable) {    // for IE11
+    var set = new Set();
+    iterable.forEach(function(v) {
+      set.add(v);
+    });
+    return set;
+  }
+
+  beforeEach(function() {
+    jasmine.getEnv().requireFunctioningSets();
+  });
+
+
+  it('matches any actual set to an empty set', function() {
+    var actualSet = new SetI(['foo', 'bar']);
+    var containing = new jasmineUnderTest.SetContaining(new Set());
+
+    expect(containing.asymmetricMatch(actualSet)).toBe(true);
+  });
+
+  it('matches when all the values in sample have matches in actual', function() {
+    var actualSet = new SetI([
+      {'foo': 'bar'}, 'baz', [1, 2, 3]
+    ]);
+
+    var containingSet = new SetI([
+      [1, 2, 3], {'foo': 'bar'}
+    ]);
+    var containing = new jasmineUnderTest.SetContaining(containingSet);
+
+    expect(containing.asymmetricMatch(actualSet)).toBe(true);
+  });
+
+  it('does not match when a value is not in actual', function() {
+    var actualSet = new SetI([
+      {'foo': 'bar'}, 'baz', [1, 2, 3]
+    ]);
+
+    var containingSet = new SetI([
+      [1, 2], {'foo': 'bar'}
+    ]);
+    var containing = new jasmineUnderTest.SetContaining(containingSet);
+
+    expect(containing.asymmetricMatch(actualSet)).toBe(false);
+  });
+
+  it('matches when all the values in sample have asymmetric matches in actual', function() {
+    var actualSet = new SetI([
+      [1, 2, 3, 4], 'other', 'foo1'
+    ]);
+
+    var containingSet = new SetI([
+      jasmine.stringMatching(/^foo\d/),
+      jasmine.arrayContaining([2, 3]),
+    ]);
+    var containing = new jasmineUnderTest.SetContaining(containingSet);
+
+    expect(containing.asymmetricMatch(actualSet)).toBe(true);
+  });
+
+  it('does not match when a value in sample has no asymmetric matches in actual', function() {
+    var actualSet = new SetI([
+      'a-foo1', [1, 2, 3, 4], 'other'
+    ]);
+
+    var containingSet = new SetI([
+      jasmine.stringMatching(/^foo\d/),
+      jasmine.arrayContaining([2, 3]),
+    ]);
+    var containing = new jasmineUnderTest.SetContaining(containingSet);
+
+    expect(containing.asymmetricMatch(actualSet)).toBe(false);
+  });
+
+  it('matches recursively', function() {
+    var actualSet = new SetI([
+      'foo', new SetI([1, 'bar', 2]), 'other'
+    ]);
+
+    var containingSet = new SetI([
+      new jasmineUnderTest.SetContaining(new SetI(['bar'])), 'foo'
+    ]);
+    var containing = new jasmineUnderTest.SetContaining(containingSet);
+
+    expect(containing.asymmetricMatch(actualSet)).toBe(true);
+  });
+
+  it('uses custom equality testers', function() {
+    function tester(a, b) {
+      // treat all negative numbers as equal
+      return (typeof a == 'number' && typeof b == 'number') ? (a < 0 && b < 0) : a === b;
+    }
+    var actualSet = new SetI(['foo', -1]);
+    var containing = new jasmineUnderTest.SetContaining(new SetI([-2, 'foo']));
+
+    expect(containing.asymmetricMatch(actualSet, [tester])).toBe(true);
+  });
+
+  it('does not match when actual is not a set', function() {
+    var containingSet = new SetI(['foo']);
+    expect(new jasmineUnderTest.SetContaining(containingSet).asymmetricMatch('foo')).toBe(false);
+    expect(new jasmineUnderTest.SetContaining(containingSet).asymmetricMatch(1)).toBe(false);
+    expect(new jasmineUnderTest.SetContaining(containingSet).asymmetricMatch(['foo'])).toBe(false);
+  });
+
+  it('throws an error when sample is not a set', function() {
+    expect(function() {
+      new jasmineUnderTest.SetContaining({'foo': 'bar'}).asymmetricMatch(new Set());
+    }).toThrowError(/You must provide a set/);
+  });
+
+  it('defines a `jasmineToString` method', function() {
+    var containing = new jasmineUnderTest.SetContaining(new Set());
+
+    expect(containing.jasmineToString()).toMatch(/^<jasmine\.setContaining/);
+  });
+});
diff --git a/spec/core/matchers/matchersUtilSpec.js b/spec/core/matchers/matchersUtilSpec.js
index f3948a32..9dd42ce5 100644
--- a/spec/core/matchers/matchersUtilSpec.js
+++ b/spec/core/matchers/matchersUtilSpec.js
@@ -290,6 +290,32 @@ describe("matchersUtil", function() {
       expect(jasmineUnderTest.matchersUtil.equals(containing, obj)).toBe(true);
     });
 
+    it("passes when MapContaining is used", function() {
+      jasmine.getEnv().requireFunctioningMaps();
+
+      var obj = new Map();
+      obj.set(1, 2);
+      obj.set('foo', 'bar');
+      var containing = new jasmineUnderTest.MapContaining(new Map());
+      containing.sample.set('foo', 'bar');
+
+      expect(jasmineUnderTest.matchersUtil.equals(obj, containing)).toBe(true);
+      expect(jasmineUnderTest.matchersUtil.equals(containing, obj)).toBe(true);
+    });
+
+    it("passes when SetContaining is used", function() {
+      jasmine.getEnv().requireFunctioningSets();
+
+      var obj = new Set();
+      obj.add(1);
+      obj.add('foo');
+      var containing = new jasmineUnderTest.SetContaining(new Set());
+      containing.sample.add(1);
+
+      expect(jasmineUnderTest.matchersUtil.equals(obj, containing)).toBe(true);
+      expect(jasmineUnderTest.matchersUtil.equals(containing, obj)).toBe(true);
+    });
+
     it("passes when an asymmetric equality tester returns true", function() {
       var tester = { asymmetricMatch: function(other) { return true; } };
 
@@ -613,6 +639,26 @@ describe("matchersUtil", function() {
       testFunction('foo', 'bar');
       expect(jasmineUnderTest.matchersUtil.contains(capturedArgs, 'bar')).toBe(true);
     });
+
+    it("passes for set members", function() {
+      jasmine.getEnv().requireFunctioningSets();
+
+      var setItem = {'foo': 'bar'};
+      var set = new Set();
+      set.add(setItem);
+
+      expect(jasmineUnderTest.matchersUtil.contains(set, setItem)).toBe(true);
+    });
+
+    // documenting current behavior
+    it("fails (!) for objects that equal to a set member", function() {
+      jasmine.getEnv().requireFunctioningSets();
+
+      var set = new Set();
+      set.add({'foo': 'bar'});
+
+      expect(jasmineUnderTest.matchersUtil.contains(set, {'foo': 'bar'})).toBe(false);
+    });
   });
 
   describe("buildMessage", function() {
diff --git a/src/core/asymmetric_equality/MapContaining.js b/src/core/asymmetric_equality/MapContaining.js
new file mode 100644
index 00000000..061c2666
--- /dev/null
+++ b/src/core/asymmetric_equality/MapContaining.js
@@ -0,0 +1,41 @@
+getJasmineRequireObj().MapContaining = function(j$) {
+  function MapContaining(sample) {
+    if (!j$.isMap(sample)) {
+      throw new Error('You must provide a map to `mapContaining`, not ' + j$.pp(sample));
+    }
+
+    this.sample = sample;
+  }
+
+  MapContaining.prototype.asymmetricMatch = function(other, customTesters) {
+    if (!j$.isMap(other)) return false;
+
+    var hasAllMatches = true;
+    j$.util.forEachBreakable(this.sample, function(breakLoop, value, key) {
+      // for each key/value pair in `sample`
+      // there should be at least one pair in `other` whose key and value both match
+      var hasMatch = false;
+      j$.util.forEachBreakable(other, function(oBreakLoop, oValue, oKey) {
+        if (
+          j$.matchersUtil.equals(oKey, key, customTesters)
+          && j$.matchersUtil.equals(oValue, value, customTesters)
+        ) {
+          hasMatch = true;
+          oBreakLoop();
+        }
+      });
+      if (!hasMatch) {
+        hasAllMatches = false;
+        breakLoop();
+      }
+    });
+
+    return hasAllMatches;
+  };
+
+  MapContaining.prototype.jasmineToString = function() {
+    return '<jasmine.mapContaining(' + j$.pp(this.sample) + ')>';
+  };
+
+  return MapContaining;
+};
diff --git a/src/core/asymmetric_equality/SetContaining.js b/src/core/asymmetric_equality/SetContaining.js
new file mode 100644
index 00000000..d9dd8fd2
--- /dev/null
+++ b/src/core/asymmetric_equality/SetContaining.js
@@ -0,0 +1,39 @@
+getJasmineRequireObj().SetContaining = function(j$) {
+  function SetContaining(sample) {
+    if (!j$.isSet(sample)) {
+      throw new Error('You must provide a set to `setContaining`, not ' + j$.pp(sample));
+    }
+
+    this.sample = sample;
+  }
+
+  SetContaining.prototype.asymmetricMatch = function(other, customTesters) {
+    if (!j$.isSet(other)) return false;
+
+    var hasAllMatches = true;
+    j$.util.forEachBreakable(this.sample, function(breakLoop, item) {
+      // for each item in `sample` there should be at least one matching item in `other`
+      // (not using `j$.matchersUtil.contains` because it compares set members by reference,
+      // not by deep value equality)
+      var hasMatch = false;
+      j$.util.forEachBreakable(other, function(oBreakLoop, oItem) {
+        if (j$.matchersUtil.equals(oItem, item, customTesters)) {
+          hasMatch = true;
+          oBreakLoop();
+        }
+      });
+      if (!hasMatch) {
+        hasAllMatches = false;
+        breakLoop();
+      }
+    });
+
+    return hasAllMatches;
+  };
+
+  SetContaining.prototype.jasmineToString = function() {
+    return '<jasmine.setContaining(' + j$.pp(this.sample) + ')>';
+  };
+
+  return SetContaining;
+};
diff --git a/src/core/base.js b/src/core/base.js
index deed4ef2..b962e129 100644
--- a/src/core/base.js
+++ b/src/core/base.js
@@ -128,6 +128,8 @@ getJasmineRequireObj().base = function(j$, jasmineGlobal) {
 
   j$.isMap = function(obj) {
     return (
+      obj !== null &&
+      typeof obj !== 'undefined' &&
       typeof jasmineGlobal.Map !== 'undefined' &&
       obj.constructor === jasmineGlobal.Map
     );
@@ -135,6 +137,8 @@ getJasmineRequireObj().base = function(j$, jasmineGlobal) {
 
   j$.isSet = function(obj) {
     return (
+      obj !== null &&
+      typeof obj !== 'undefined' &&
       typeof jasmineGlobal.Set !== 'undefined' &&
       obj.constructor === jasmineGlobal.Set
     );
@@ -279,6 +283,32 @@ getJasmineRequireObj().base = function(j$, jasmineGlobal) {
     return new j$.ArrayWithExactContents(sample);
   };
 
+  /**
+   * Get a matcher, usable in any {@link matchers|matcher} that uses Jasmine's equality (e.g. {@link matchers#toEqual|toEqual}, {@link matchers#toContain|toContain}, or {@link matchers#toHaveBeenCalledWith|toHaveBeenCalledWith}),
+   * that will succeed if every key/value pair in the sample passes the deep equality comparison
+   * with at least one key/value pair in the actual value being compared
+   * @name jasmine.mapContaining
+   * @since
+   * @function
+   * @param {Map} sample - The subset of items that _must_ be in the actual.
+   */
+  j$.mapContaining = function(sample) {
+    return new j$.MapContaining(sample);
+  };
+
+  /**
+   * Get a matcher, usable in any {@link matchers|matcher} that uses Jasmine's equality (e.g. {@link matchers#toEqual|toEqual}, {@link matchers#toContain|toContain}, or {@link matchers#toHaveBeenCalledWith|toHaveBeenCalledWith}),
+   * that will succeed if every item in the sample passes the deep equality comparison
+   * with at least one item in the actual value being compared
+   * @name jasmine.mapContaining
+   * @since
+   * @function
+   * @param {Set} sample - The subset of items that _must_ be in the actual.
+   */
+  j$.setContaining = function(sample) {
+    return new j$.SetContaining(sample);
+  };
+
   j$.isSpy = function(putativeSpy) {
     if (!putativeSpy) {
       return false;
diff --git a/src/core/matchers/matchersUtil.js b/src/core/matchers/matchersUtil.js
index 14647dd6..cfc0c749 100644
--- a/src/core/matchers/matchersUtil.js
+++ b/src/core/matchers/matchersUtil.js
@@ -7,7 +7,7 @@ getJasmineRequireObj().matchersUtil = function(j$) {
     contains: function(haystack, needle, customTesters) {
       customTesters = customTesters || [];
 
-      if ((Object.prototype.toString.apply(haystack) === '[object Set]')) {
+      if (j$.isSet(haystack)) {
         return haystack.has(needle);
       }
 
diff --git a/src/core/requireCore.js b/src/core/requireCore.js
index d6b98eb5..a2c5f177 100644
--- a/src/core/requireCore.js
+++ b/src/core/requireCore.js
@@ -55,6 +55,8 @@ var getJasmineRequireObj = (function(jasmineGlobal) {
     j$.ObjectContaining = jRequire.ObjectContaining(j$);
     j$.ArrayContaining = jRequire.ArrayContaining(j$);
     j$.ArrayWithExactContents = jRequire.ArrayWithExactContents(j$);
+    j$.MapContaining = jRequire.MapContaining(j$);
+    j$.SetContaining = jRequire.SetContaining(j$);
     j$.pp = jRequire.pp(j$);
     j$.QueueRunner = jRequire.QueueRunner(j$);
     j$.ReportDispatcher = jRequire.ReportDispatcher(j$);
diff --git a/src/core/util.js b/src/core/util.js
index 0c25382a..4118deec 100644
--- a/src/core/util.js
+++ b/src/core/util.js
@@ -133,5 +133,24 @@ getJasmineRequireObj().util = function(j$) {
     };
   })();
 
+  function StopIteration() {}
+  StopIteration.prototype = Object.create(Error.prototype);
+  StopIteration.prototype.constructor = StopIteration;
+
+  // useful for maps and sets since `forEach` is the only IE11-compatible way to iterate them
+  util.forEachBreakable = function(iterable, iteratee) {
+    function breakLoop() {
+      throw new StopIteration();
+    }
+
+    try {
+      iterable.forEach(function(value, key) {
+        iteratee(breakLoop, value, key, iterable);
+      });
+    } catch (error) {
+      if (!(error instanceof StopIteration)) throw error;
+    }
+  };
+
   return util;
 };