diff --git a/pkgs/racket-doc/scribblings/reference/pairs.scrbl b/pkgs/racket-doc/scribblings/reference/pairs.scrbl
index fa75e3b11e..fdc6e24f5a 100644
--- a/pkgs/racket-doc/scribblings/reference/pairs.scrbl
+++ b/pkgs/racket-doc/scribblings/reference/pairs.scrbl
@@ -1221,6 +1221,33 @@ result of @racket[proc].  Signals an error on an empty list.
   (argmax car '((3 pears) (3 oranges)))]}
 
 
+@defproc[(group-by [key (-> any/c any/c)]
+                   [lst list?]
+                   [same? (any/c any/c . -> . any/c) equal?])
+         (listof list?)]{
+
+Groups the given list into equivalence classes, with equivalence being
+determined by @racket[same?]. Within each equivalence class, @racket[group-by]
+preserves the ordering of the original list. Equivalence classes themselves are
+in order of first appearance in the input.
+
+@examples[#:eval list-eval
+(group-by (lambda (x) (modulo x 3)) '(1 2 1 2 54 2 5 43 7 2 643 1 2 0))
+]
+}
+
+@defproc[(cartesian-product [lst list?] ...)
+         (listof list?)]{
+
+Computes the n-ary cartesian product of the given lists.
+
+@examples[#:eval list-eval
+(cartesian-product '(1 2 3) '(a b c))
+(cartesian-product '(4 5 6) '(d e f) '(#t #f))
+]
+}
+
+
 @close-eval[list-eval]
 
 
diff --git a/pkgs/racket-test-core/tests/racket/list.rktl b/pkgs/racket-test-core/tests/racket/list.rktl
index 55d1ca3e41..539328802e 100644
--- a/pkgs/racket-test-core/tests/racket/list.rktl
+++ b/pkgs/racket-test-core/tests/racket/list.rktl
@@ -540,4 +540,31 @@
   (test '(20 19 18 17 16 15 14 13 12 11) range 20 10 -1)
   (test '(10 11.5 13.0 14.5) range 10 15 1.5))
 
+;; ---------- group-by ----------
+
+(test '((1) (4) (2 2) (56) (3)) group-by values '(1 4 2 56 2 3))
+(test '((1 1 1) (2 2 2 2 2) (54) (5) (43) (7) (643) (0))
+      group-by values '(1 2 1 2 54 2 5 43 7 2 643 1 2 0))
+(test '((1 3) (4 2 56 2))
+      group-by values '(1 4 2 56 2 3) (lambda (x y) (or (and (even? x) (even? y))
+                                                        (and (odd?  x) (odd?  y)))))
+(test '(((1 a)) ((4 b)) ((2 c) (2 e)) ((56 d)) ((3 f)))
+      group-by car '((1 a) (4 b) (2 c) (56 d) (2 e) (3 f)))
+(test '((1 3 5) (2 4 6)) group-by even? '(1 2 3 4 5 6))
+(err/rt-test (group-by #f))
+(err/rt-test (group-by '() #f))
+(err/rt-test (group-by '() values #f))
+
+;; ---------- cartesian-product ----------
+
+(test '((1 a) (1 b) (1 c)
+        (2 a) (2 b) (2 c)
+        (3 a) (3 b) (3 c))
+      cartesian-product '(1 2 3) '(a b c))
+(test '((4 d #t) (4 d #f) (4 e #t) (4 e #f) (4 f #t) (4 f #f)
+        (5 d #t) (5 d #f) (5 e #t) (5 e #f) (5 f #t) (5 f #f)
+        (6 d #t) (6 d #f) (6 e #t) (6 e #f) (6 f #t) (6 f #f))
+      cartesian-product '(4 5 6) '(d e f) '(#t #f))
+(err/rt-test (cartesian-product 3))
+
 (report-errs)
diff --git a/racket/collects/racket/list.rkt b/racket/collects/racket/list.rkt
index b0ffde536b..838d64a9a3 100644
--- a/racket/collects/racket/list.rkt
+++ b/racket/collects/racket/list.rkt
@@ -40,7 +40,9 @@
          permutations
          in-permutations
          argmin
-         argmax)
+         argmax
+         group-by
+         cartesian-product)
 
 (define (first x)
   (if (and (pair? x) (list? x))
@@ -611,3 +613,65 @@
               (loop min min-var (cdr xs))]))]))))
 (define (argmin f xs) (mk-min < 'argmin f xs))
 (define (argmax f xs) (mk-min > 'argmax f xs))
+
+;; (x -> y) (listof x) [(y y -> bool)] -> (listof (listof x))
+;; groups together elements that are considered equal
+;; =? should be reflexive, transitive and commutative
+(define (group-by key l [=? equal?])
+
+  (unless (and (procedure? key)
+               (procedure-arity-includes? key 1))
+    (raise-argument-error 'group-by "(-> any/c any/c)" key))
+  (unless (and (procedure? =?)
+               (procedure-arity-includes? =? 2))
+    (raise-argument-error 'group-by "(any/c any/c . -> . any/c)" =?))
+  (unless (list? l)
+    (raise-argument-error 'group-by "list?" l))
+
+  ;; like hash-update, but for alists
+  (define (alist-update al k up fail)
+    (let loop ([al al])
+      (cond [(null? al)
+             ;; did not find equivalence class, create one
+             (list (cons k (up '())))]
+            [(=? (car (car al)) k)
+             ;; found the right equivalence class
+             (cons
+              (cons k (up (cdr (car al)))) ; updater takes elements, w/o key
+              (cdr al))]
+            [else ; keep going
+             (cons (car al) (loop (cdr al)))])))
+
+  ;; In cases where `=?` is a built-in equality, can use hash tables instead
+  ;; of lists to compute equivalence classes.
+  (define-values (base update)
+    (cond [(equal? =? eq?)    (values (hasheq)  hash-update)]
+          [(equal? =? eqv?)   (values (hasheqv) hash-update)]
+          [(equal? =? equal?) (values (hash)    hash-update)]
+          [else               (values '()       alist-update)]))
+
+  (define classes
+    (for/fold ([res base])
+        ([elt (in-list l)]
+         [idx (in-naturals)]) ; to keep ordering stable
+      (define k (key elt))
+      (define v (cons idx elt))
+      (update res k (lambda (o) (cons v o)) '())))
+  (define sorted-classes
+    (if (list? classes)
+        (for/list ([p (in-list classes)])
+          (sort (cdr p) < #:key car))
+        (for/list ([(_ c) (in-hash classes)])
+          (sort c < #:key car))))
+  ;; sort classes by order of first appearance, then remove indices
+  (for/list ([c (in-list (sort sorted-classes < #:key caar))])
+    (map cdr c)))
+
+;; (listof x) ... -> (listof (listof x))
+(define (cartesian-product . ls)
+  (for ([l (in-list ls)])
+    (unless (list? l)
+      (raise-argument-error 'cartesian-product "list?" l)))
+  (define (cp-2 as bs)
+    (for*/list ([i (in-list as)] [j (in-list bs)]) (cons i j)))
+  (foldr cp-2 (list (list)) ls))