diff --git a/lib/assert.js b/lib/assert.js
index df575c0f169b22..2eac9f73987f25 100644
--- a/lib/assert.js
+++ b/lib/assert.js
@@ -161,6 +161,14 @@ function isArguments(tag) {
   return tag === '[object Arguments]';
 }
 
+function isMap(object) {
+  return object.constructor === Map;
+}
+
+function isSet(object) {
+  return object.constructor === Set;
+}
+
 function _deepEqual(actual, expected, strict, memos) {
   // All identical values are equivalent, as determined by ===.
   if (actual === expected) {
@@ -262,11 +270,18 @@ function _deepEqual(actual, expected, strict, memos) {
     }
   }
 
-  // For all other Object pairs, including Array objects,
+  if (isSet(actual)) {
+    return isSet(expected) && setEquiv(actual, expected);
+  } else if (isSet(expected)) {
+    return false;
+  }
+
+  // For all other Object pairs, including Array objects and Maps,
   // equivalence is determined by having:
   // a) The same number of owned enumerable properties
   // b) The same set of keys/indexes (although not necessarily the same order)
   // c) Equivalent values for every corresponding key/index
+  // d) For Maps, strict-equal keys mapping to deep-equal values
   // Note: this accounts for both named and indexed properties on Arrays.
 
   // Use memos to handle cycles.
@@ -283,6 +298,26 @@ function _deepEqual(actual, expected, strict, memos) {
   return objEquiv(actual, expected, strict, memos);
 }
 
+function setEquiv(a, b) {
+  // This behaviour will work for any sets with contents that have
+  // strict-equality. That is, it will return false if the two sets contain
+  // equivalent objects that aren't reference-equal. We could support that, but
+  // it would require scanning each pairwise set of not strict-equal items,
+  // which is O(n^2), and would get exponentially worse if sets are nested. So
+  // for now we simply won't support deep equality checking set items or map
+  // keys.
+  if (a.size !== b.size)
+    return false;
+
+  var val;
+  for (val of a) {
+    if (!b.has(val))
+      return false;
+  }
+
+  return true;
+}
+
 function objEquiv(a, b, strict, actualVisitedObjects) {
   // If one of them is a primitive, the other must be the same.
   if (util.isPrimitive(a) || util.isPrimitive(b))
@@ -307,6 +342,25 @@ function objEquiv(a, b, strict, actualVisitedObjects) {
       return false;
   }
 
+  if (isMap(a)) {
+    if (!isMap(b))
+      return false;
+
+    if (a.size !== b.size)
+      return false;
+
+    var item;
+    for ([key, item] of a) {
+      if (!b.has(key))
+        return false;
+
+      if (!_deepEqual(item, b.get(key), strict, actualVisitedObjects))
+        return false;
+    }
+  } else if (isMap(b)) {
+    return false;
+  }
+
   // The pair must have equivalent values for every corresponding key.
   // Possibly expensive deep test:
   for (i = aKeys.length - 1; i >= 0; i--) {
diff --git a/test/parallel/test-assert-deep.js b/test/parallel/test-assert-deep.js
index 395f9c36f7c688..2ae6469fe5179f 100644
--- a/test/parallel/test-assert-deep.js
+++ b/test/parallel/test-assert-deep.js
@@ -107,4 +107,105 @@ for (const a of similar) {
   }
 }
 
+function assertDeepAndStrictEqual(a, b) {
+  assert.doesNotThrow(() => assert.deepEqual(a, b));
+  assert.doesNotThrow(() => assert.deepStrictEqual(a, b));
+
+  assert.doesNotThrow(() => assert.deepEqual(b, a));
+  assert.doesNotThrow(() => assert.deepStrictEqual(b, a));
+}
+
+function assertNotDeepOrStrict(a, b) {
+  assert.throws(() => assert.deepEqual(a, b));
+  assert.throws(() => assert.deepStrictEqual(a, b));
+
+  assert.throws(() => assert.deepEqual(b, a));
+  assert.throws(() => assert.deepStrictEqual(b, a));
+}
+
+// es6 Maps and Sets
+assertDeepAndStrictEqual(new Set(), new Set());
+assertDeepAndStrictEqual(new Map(), new Map());
+
+// deepEqual only works with primitive key values and reference-equal values in
+// sets and map keys avoid O(n^d) complexity (where d is depth)
+assertDeepAndStrictEqual(new Set([1, 2, 3]), new Set([1, 2, 3]));
+assertNotDeepOrStrict(new Set([1, 2, 3]), new Set([1, 2, 3, 4]));
+assertNotDeepOrStrict(new Set([1, 2, 3, 4]), new Set([1, 2, 3]));
+assertDeepAndStrictEqual(new Set(['1', '2', '3']), new Set(['1', '2', '3']));
+
+assertDeepAndStrictEqual(new Map([[1, 1], [2, 2]]), new Map([[1, 1], [2, 2]]));
+assertDeepAndStrictEqual(new Map([[1, 1], [2, 2]]), new Map([[2, 2], [1, 1]]));
+assertNotDeepOrStrict(new Map([[1, 1], [2, 2]]), new Map([[1, 2], [2, 1]]));
+
+assertNotDeepOrStrict(new Set([1]), [1]);
+assertNotDeepOrStrict(new Set(), []);
+assertNotDeepOrStrict(new Set(), {});
+
+assertNotDeepOrStrict(new Map([['a', 1]]), {a: 1});
+assertNotDeepOrStrict(new Map(), []);
+assertNotDeepOrStrict(new Map(), {});
+
+{
+  const values = [
+    123,
+    Infinity,
+    0,
+    null,
+    undefined,
+    false,
+    true,
+    {}, // Objects, lists and functions are ok if they're in by reference.
+    [],
+    () => {},
+  ];
+  assertDeepAndStrictEqual(new Set(values), new Set(values));
+  assertDeepAndStrictEqual(new Set(values), new Set(values.reverse()));
+
+  const mapValues = values.map((v) => [v, {a: 5}]);
+  assertDeepAndStrictEqual(new Map(mapValues), new Map(mapValues));
+  assertDeepAndStrictEqual(new Map(mapValues), new Map(mapValues.reverse()));
+}
+
+{
+  const s1 = new Set();
+  const s2 = new Set();
+  s1.add(1);
+  s1.add(2);
+  s2.add(2);
+  s2.add(1);
+  assertDeepAndStrictEqual(s1, s2);
+}
+
+{
+  const m1 = new Map();
+  const m2 = new Map();
+  const obj = {a: 5, b: 6};
+  m1.set(1, obj);
+  m1.set(2, 'hi');
+  m1.set(3, [1, 2, 3]);
+
+  m2.set(2, 'hi'); // different order
+  m2.set(1, obj);
+  m2.set(3, [1, 2, 3]); // deep equal, but not reference equal.
+
+  assertDeepAndStrictEqual(m1, m2);
+}
+
+{
+  const m1 = new Map();
+  const m2 = new Map();
+
+  // m1 contains itself.
+  m1.set(1, m1);
+  m2.set(1, new Map());
+
+  assertNotDeepOrStrict(m1, m2);
+}
+
+assert.deepEqual(new Map([[1, 1]]), new Map([[1, '1']]));
+assert.throws(() =>
+  assert.deepStrictEqual(new Map([[1, 1]]), new Map([[1, '1']]))
+);
+
 /* eslint-enable */