diff --git a/lib/jasmine-core/jasmine.js b/lib/jasmine-core/jasmine.js
index ca636eca..d05ae562 100644
--- a/lib/jasmine-core/jasmine.js
+++ b/lib/jasmine-core/jasmine.js
@@ -77,6 +77,8 @@ 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$.ReportDispatcher = jRequire.ReportDispatcher(j$);
@@ -283,6 +285,8 @@ getJasmineRequireObj().base = function(j$, jasmineGlobal) {
 
   j$.isMap = function(obj) {
     return (
+      obj !== null &&
+      typeof obj !== 'undefined' &&
       typeof jasmineGlobal.Map !== 'undefined' &&
       obj.constructor === jasmineGlobal.Map
     );
@@ -290,6 +294,8 @@ getJasmineRequireObj().base = function(j$, jasmineGlobal) {
 
   j$.isSet = function(obj) {
     return (
+      obj !== null &&
+      typeof obj !== 'undefined' &&
       typeof jasmineGlobal.Set !== 'undefined' &&
       obj.constructor === jasmineGlobal.Set
     );
@@ -434,6 +440,32 @@ getJasmineRequireObj().base = function(j$, 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$.isSpy = function(putativeSpy) {
     if (!putativeSpy) {
       return false;
@@ -580,6 +612,25 @@ getJasmineRequireObj().util = function(j$) {
     };
   })();
 
+  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;
 };
 
@@ -2247,6 +2298,48 @@ getJasmineRequireObj().Falsy = function(j$) {
   return Falsy;
 };
 
+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$.pp(this.sample) + ')>';
+  };
+
+  return MapContaining;
+};
+
 getJasmineRequireObj().NotEmpty = function (j$) {
 
   function NotEmpty() {}
@@ -2324,6 +2417,46 @@ getJasmineRequireObj().ObjectContaining = function(j$) {
   return ObjectContaining;
 };
 
+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$.pp(this.sample) + ')>';
+  };
+
+  return SetContaining;
+};
+
 getJasmineRequireObj().StringMatching = function(j$) {
 
   function StringMatching(expected) {
@@ -3860,7 +3993,7 @@ 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);
       }
 
@@ -5624,11 +5757,16 @@ getJasmineRequireObj().pp = function(j$) {
   function hasCustomToString(value) {
     // value.toString !== Object.prototype.toString if value has no custom toString but is from another context (e.g.
     // iframe, web worker)
-    return (
-      j$.isFunction_(value.toString) &&
-      value.toString !== Object.prototype.toString &&
-      value.toString() !== Object.prototype.toString.call(value)
-    );
+    try {
+      return (
+        j$.isFunction_(value.toString) &&
+        value.toString !== Object.prototype.toString &&
+        value.toString() !== Object.prototype.toString.call(value)
+      );
+    } catch (e) {
+      // The custom toString() threw.
+      return true;
+    }
   }
 
   PrettyPrinter.prototype.format = function(value) {
@@ -5674,7 +5812,11 @@ getJasmineRequireObj().pp = function(j$) {
         !j$.isArray_(value) &&
         hasCustomToString(value)
       ) {
-        this.emitScalar(value.toString());
+        try {
+          this.emitScalar(value.toString());
+        } catch (e) {
+          this.emitScalar('has-invalid-toString-method');
+        }
       } else if (j$.util.arrayContains(this.seen, value)) {
         this.emitScalar(
           '<circular reference: ' +
diff --git a/spec/core/PrettyPrintSpec.js b/spec/core/PrettyPrintSpec.js
index 0e3c48ad..1249d8c6 100644
--- a/spec/core/PrettyPrintSpec.js
+++ b/spec/core/PrettyPrintSpec.js
@@ -457,11 +457,17 @@ describe('jasmineUnderTest.pp', function() {
       // Valid: an actual number
       baz: 3,
       // Valid: an actual Error object
-      qux: new Error('bar')
+      qux: new Error('bar'),
+      //
+      baddy: {
+        toString: function() {
+          throw new Error('I am a bad toString');
+        }
+      }
     };
 
     expect(jasmineUnderTest.pp(obj)).toEqual(
-      'Object({ foo: [object Number], bar: [object Object], baz: 3, qux: Error: bar })'
+      'Object({ foo: [object Number], bar: [object Object], baz: 3, qux: Error: bar, baddy: has-invalid-toString-method })'
     );
   });
 });
diff --git a/src/core/PrettyPrinter.js b/src/core/PrettyPrinter.js
index 67cb34d6..e01afc80 100644
--- a/src/core/PrettyPrinter.js
+++ b/src/core/PrettyPrinter.js
@@ -9,11 +9,16 @@ getJasmineRequireObj().pp = function(j$) {
   function hasCustomToString(value) {
     // value.toString !== Object.prototype.toString if value has no custom toString but is from another context (e.g.
     // iframe, web worker)
-    return (
-      j$.isFunction_(value.toString) &&
-      value.toString !== Object.prototype.toString &&
-      value.toString() !== Object.prototype.toString.call(value)
-    );
+    try {
+      return (
+        j$.isFunction_(value.toString) &&
+        value.toString !== Object.prototype.toString &&
+        value.toString() !== Object.prototype.toString.call(value)
+      );
+    } catch (e) {
+      // The custom toString() threw.
+      return true;
+    }
   }
 
   PrettyPrinter.prototype.format = function(value) {
@@ -59,7 +64,11 @@ getJasmineRequireObj().pp = function(j$) {
         !j$.isArray_(value) &&
         hasCustomToString(value)
       ) {
-        this.emitScalar(value.toString());
+        try {
+          this.emitScalar(value.toString());
+        } catch (e) {
+          this.emitScalar('has-invalid-toString-method');
+        }
       } else if (j$.util.arrayContains(this.seen, value)) {
         this.emitScalar(
           '<circular reference: ' +