diff --git a/lib/assert.js b/lib/assert.js
index ea142ed01f8f6e..ef49f251bab497 100644
--- a/lib/assert.js
+++ b/lib/assert.js
@@ -185,6 +185,36 @@ function isArguments(object) {
   return Object.prototype.toString.call(object) == '[object Arguments]';
 }
 
+function compareMaps(a, b, strict) {
+  // check size of the maps
+  if (a.size !== b.size)
+    return false;
+
+  // iterate over all keys and check if they exist in the other
+  for (let kvs of a) {
+    const key = kvs[0];
+    const val = kvs[1];
+    if (!b.has(key)) {
+      return false;
+    }
+
+    if (!_deepEqual(val, b.get(key), strict))
+      return false;
+  }
+  return true;
+}
+
+function compareSets(a, b) {
+  if (a.size !== b.size)
+    return false;
+
+  for (let item of a) {
+    if (!b.has(item))
+      return false;
+  }
+  return true;
+}
+
 function objEquiv(a, b, strict) {
   if (a === null || a === undefined || b === null || b === undefined)
     return false;
@@ -202,6 +232,13 @@ function objEquiv(a, b, strict) {
     b = pSlice.call(b);
     return _deepEqual(a, b, strict);
   }
+  const aStr = Object.prototype.toString.call(a);
+  const bStr = Object.prototype.toString.call(b);
+  if (aStr === '[object Map]' && bStr === '[object Map]') {
+    return compareMaps(a, b, strict);
+  } else if (aStr === '[object Set]' && bStr === '[object Set]') {
+    return compareSets(a, b);
+  }
   var ka = Object.keys(a),
       kb = Object.keys(b),
       key, i;
diff --git a/test/parallel/test-assert.js b/test/parallel/test-assert.js
index ce84eabc34e1d4..ed99b01f91ec69 100644
--- a/test/parallel/test-assert.js
+++ b/test/parallel/test-assert.js
@@ -465,4 +465,63 @@ testBlockTypeError(assert.doesNotThrow, null);
 testBlockTypeError(assert.throws, undefined);
 testBlockTypeError(assert.doesNotThrow, undefined);
 
+// Map deep equal, deep strict equal
+const map1 = new Map();
+const map2 = new Map();
+map1.set('1', '2');
+map2.set('1', '2');
+assert.deepEqual(map1, map2);
+map1.set('2', '2');
+assert.throws(function() {
+  assert.deepEqual(map1, map2);
+});
+map1.delete('2');
+map2.set('1', 2);
+assert.deepEqual(map1, map2);
+assert.throws(function() {
+  assert.deepStrictEqual(map1, map2);
+});
+map1.clear();
+map2.clear();
+map1.set(NaN, 'not a number');
+map2.set(NaN, 'not a number');
+assert.deepEqual(map1, map2);
+map1.clear();
+map2.clear();
+map1.set('1', { name: 'test' });
+map2.set('1', { name: 'test' });
+assert.deepStrictEqual(map1, map2);
+map1.clear();
+map2.clear();
+// verify that insertion order doesn't matter
+map1.set('1', '1');
+map1.set('2', '2');
+map2.set('2', '2');
+map2.set('1', '1');
+assert.deepEqual(map1, map2);
+
+// Set deep equal, deep strict equal
+var set1 = new Set();
+var set2 = new Set();
+set1.add(1);
+set2.add(1);
+assert.deepEqual(set1, set2);
+set1.add(2);
+assert.throws(function() {
+  assert.deepEqual(set1, set2);
+});
+set1.delete(2);
+set2.delete(1);
+set2.add('1');
+// throws because we can't really check without being strict
+assert.throws(function() {
+  assert.deepEqual(set1, set2);
+});
+
+assert.deepEqual(new Set([NaN]), new Set([NaN]));
+// verify that insertion order doesn't matter
+set1 = new Set([1, 2]);
+set2 = new Set([2, 1]);
+assert.deepEqual(set1, set2);
+
 console.log('All OK');