January 9 – Leon Trotsky begins exile in Mexico with his wife Natalia Sedova; they share The Blue House in Coyoacán with painters Frida Kahlo and Diego Rivera and Trotsky has an affair with Frida.
May–June – Pablo Picasso paints Guernica, a cubistic mural created in reaction to the German bombing of the Spanish Basque town of the same name on 26 April. It is first exhibited in July at the Spanish Republican government pavilion (designed by Josep Lluís Sert) in the Exposition Internationale des Arts et Techniques dans la Vie Moderne in Paris before commencing a world tour. René Iché created a sculpture Guernica the day after the bombing took place, but will not exhibit it in his lifetime. The Spanish Government pavilion at the International Exhibition also includes Horacio Ferrer's Madrid 1937 (Black Aeroplanes), Joan Miró's The Reaper and a mercury fountain by Alexander Calder. Vera Mukhina's sculpture Worker and Kolkhoz Woman is also created for the Exhibition.
May – Stanley Spencer and his wife Hilda are divorced; within a week he marries Patricia Preece who departs on honeymoon to St Ives with her partner Dorothy Hepworth while he resumes relations with Hilda at Cookham.
July 18 – Große Deutsche Kunstausstellung ("Great German Art Exhibition") opened by Adolf Hitler in the Haus der deutschen Kunst ("House of German Art") in Munich, newly completed to the designs of Paul Troost (d. 1934) to display art of the Third Reich. Hitler has rejected the choices of the original selection jury and placed his personal photographer Heinrich Hoffmann in charge of curating the display, but even so has rejected some of the more experimental paintings.
July 19 – Entartete Kunst ("Degenerate art") exhibition, mounted by the Nazis, opens in Munich.
October – Formation in London of the Euston Road School, a private School of Drawing and Painting originally established in Fitzroy Street by William Coldstream, Claude Rogers and Victor Pasmore, and giving name to the group of naturalist artists associated with it.
December 21 – Premiere of Walt Disney's Snow White and the Seven Dwarfs in the United States, the first full-length animated feature film (concept artist: Albert Hurter).
The exhibition The Origins and Development of International Independent Art held at the Galerie nationale du Jeu de Paume in Paris brings Chaim Soutine to prominence.
The Avant-Garde Image Group is founded by Japanese photographer Terushichi Hirai.
American painters Paul Cadmus, Jared French and Margaret French (née Hoening) form the PaJaMa photographic collective.
Statues by Jacob Epstein on Rhodesia House, London, are mutilated.
1937–1938 – Mussolini has the Ara Pacis Augustae reconstructed in its present location.
Endre Bálint – My Room at the Bindendorfs
Balthus – The Mountain
William Coldstream – Winifred Burger
The Burning Giraffe
Metamorphosis of Narcissus, a surrealist work influenced by the Greek myth of Narcissus
Swans Reflecting Elephants
Edwin Dickinson – Composition with Still Life
Óscar Domínguez – The Infernal Machine
Max Dupain – Sunbaker
Arthur Dove – Me and the Moon
M. C. Escher – woodcuts
Still Life and Street, his first impossible reality
Alberto Giacometti – The Artist's Mother
Gluck – Medallion
Herman Otto Hoyer – Am Anfang war das Wort ("In the beginning was the word")
Gladys Hynes – Private View
The Deceased Dimas
Me and My Doll
Memory - the heart
My Nurse and I
Self-portrait dedicated to Leon Trotsky between the curtains
Self-portrait as a degenerate artist
The Black Flag
Not to be Reproduced
On the Threshold of Liberty
Lady in Blue
Robe violette et Anémones
Woman in a Purple Coat
Yellow Odalisque (second version, Philadelphia Museum of Art)
Naked woman climbing a staircase
Still Life with Old Shoe
Georgia O'Keeffe – Jimson Weed
The Weeping Woman
Woman in Hat and Fur Collar
The South Indian Villagers
Stanley Spencer – Double Nude Portrait: The Artist and his Second Wife
Rex Whistler – Dining room mural, Plas Newydd, Anglesey
Adolf Ziegler – Die vier Elemente ("The Four Elements", triptych)
H. S. Wong – Bloody Saturday (photograph)
Franz Ehrlich – Gates to Buchenwald concentration camp
John Gregory – Anthony Wayne
A. F. Hardiman – Earl Haig Memorial
René Iché – Guernica
Charles Keck – Father Duffy (bronze, Duffy Square, New York City)
Lee Lawrie – Atlas
Ronald Moody – Midonz (carved wood head)
Vera Mukhina – Worker and Kolkhoz Woman
Edith Barretto Stevens Parsons – Frog Baby Fountain
Archibald Prize: Normand Baker – Self Portrait
March 23 – Parviz Tanavoli, Iranian-born sculptor
May 31 – Larry Zox, American painter and printmaker (d.2006)
June 7 – Red Grooms, born Charles Rogers Grooms, American multimedia pop artist
July 9 – David Hockney, English painter
August 2 – John Salt, English painter
August 18 – Willie Rushton, English cartoonist, satirist, comedian, actor and performer (d.1996)
October 1 – Larry Poons, Japanese-born American op artist
October 6 – Fritz Scholder, Native American painter, printmaker and graphic artist (d.2005)
October 12 – Robert Mangold, American minimalist painter
October 19 – Peter Max, German-born American printmaker and graphic designer
December 16 – Edward Ruscha, American painter, printmaker, photographer and conceptual artist
full date unknown – Ronald Davis, American painter
January 29 – Marc-Aurèle de Foy Suzor-Coté, Canadian painter and sculptor (b. 1869)
February 11 – Suzette Holten, Danish painter and ceramist (born 1863)
February 28 – Harrington Mann, Scottish-born portrait painter and decorative artist in the United States (b. 1864)
March 9 – Alfred Flechtheim, German-born art dealer, collector and publisher (b. 1878)
March 12 – Eveleen Tennant Myers, English portrait photographer (b. 1856)
April 19 – Martin Conway, English art critic (b. 1856)
May – Peter Waals, Dutch-born furniture designer (b. 1870)
October 29 – Élie Faure, French art historian (b. 1873)
November 6 – Colin Campbell Cooper, American painter (b. 1856)
November 11 – Helen Thornycroft, English painter (b. 1848)
December 5 – János Thorma, Hungarian Post-Impressionist painter (b. 1870)
Francis Cadell, Scottish Colourist painter (b. 1883)
Florence Griswold, American curator (b. 1850)
1937 in art Wikipedia