Events from the year 1756 in art.
- Richard Trevor, Prince Bishop of Durham, acquires 13 paintings by Francisco de Zurbarán depicting the patriarch Jacob and 12 of his sons for his palace at Auckland Castle in north east England.
- François Boucher paints portraits of Madame de Pompadour.
- John Singleton Copley paints pictures with Rococo influence.
- Szymon Czechowicz paints Bishop Stanislaus bringing back to life Piotrawin.
- Thomas Gainsborough paints The Painter's Daughters Chasing a Butterfly
- Joshua Reynolds paints portraits of Susanna Beckford and Captain Robert Orme.
- Johan Zoffany paints his Self-portrait as David with the head of Goliath (approximate date).
- January 6 – Gaspare Landi, Italian Neoclassical painter (died 1830)
- February 12 – Joseph Chinard, French sculptor who worked in a Neoclassical style (died 1813)
- March 4 – Henry Raeburn, Scottish portrait painter (died 1823)
- April 26 – Johann Friedrich Dryander, German-born portrait painter (died 1812)
- May 23 – Charles Clément Balvay, French engraver mainly working in intaglio and exclusively in burin (died 1822)
- June 3 – Louis-François Cassas, French landscape painter, sculptor and architect (died 1827)
- June 6 – John Trumbull, American painter (died 1843)
- July 14 – Thomas Rowlandson, English artist and caricaturist (died 1827)
- August 13 – James Gillray, British caricaturist (died 1815)
- October 22 - Samuel Alken, English sculptor and engraver (died 1815)
- December 7 – Cornelis van Spaendonck, Dutch painter (died 1839)
- December 17 – Edme Quenedey des Ricets, French painter and engraver, especially miniatures (died 1830)
- date unknown
- Gaspard Duché de Vancy, French painter and drawer (died 1788)
- Thomas Gaugain, English stipple engraver (died 1812)
- John Hickey, Irish-born sculptor (died 1795)
- Grigory Ostrovsky, Russian portraitist (died 1814)
- Hugh Robinson, British history and portrait painter (died 1796)
- (b. 1756/1758) – Francesco Piranesi, Italian engraver and architect (died 1810)
- January 25 – Christoph Thomas Scheffler, German Rococo painter (born 1699)
- May 2 - John Faber Junior, Dutch portrait engraver (born c.1695)
- July 24 – George Vertue, English engraver and antiquary (born 1684)
- November 21 – José de Ibarra, Mexican painter (born 1688)
- date unknown
- Gillray, James (1966). Hill, Draper (ed.). Fashionable contrasts: caricatures. London: Phaidon. p. 8.