Events from the year 1721 in art.

• The Ascension Convent in Moscow is renovated by order of Tsar Peter I of Russia.

• Antoine Watteau – Pilgrimage to Cythera

• January 17 – Charles Germain de Saint Aubin, draftsman and embroidery designer to King Louis XV (died 1786)
• August 10 – Dirk van der Burg, Dutch artist, landscape painter and watercolourist (died 1773)
• date unknown
  • Francesco Albotto, Italian painter (died 1757)
  • Jean Charles Baquoy, French engraver (died 1777)
  • Charles Joseph Flipart, French painter and engraver (died 1797)
  • Charles Grignion the Elder, British engraver and draughtsman (died 1810)
  • Pietro Antonio Lorenzoni, Italian portrait painter (died 1782)

• April 20 – Louis Laguerre, French decorative painter working in England (born 1663)
• July 18 – Antoine Watteau, painter (born 1684)
• August 3 – Grinling Gibbons, English master wood carver (born 1648)
• September 3 - Benoît Audran the Elder, French engraver (born 1661)
• December 19 – Bonaventura Lamberti, Italian painter active mainly in Rome (born 1653)
• date unknown
  • Giovanni Lorenzo Bertolotti, Italian painter active in Genoa (born 1640)
  • Francesco Antonio Caneti, Italian miniature painter (born 1652)
  • Andrea dell'Asta, Italian painter (born 1673)
  • John Faber the Elder, Dutch portrait engraver active in London (born 1660)
  • Luigi Garzi, Italian painter (born 1638)
  • Giuseppe Ghezzi, Italian painter, active mainly in Rome (born 1634)
  • Nicola Malinconico, Neapolitan painter (born 1663)
  • Jose Risueño, Spanish painter who helped decorate the cupola of the church in the Carthusian monastery (born 1640)