In 1915, Malevich laid down the foundations of Suprematism when he published his manifesto, From Cubism to Suprematism. In 1916–1917 he participated in exhibitions of the Jack of Diamonds group in Moscow together with Nathan Altman, David Burliuk, Alexandra Exter and others. Famous examples of his Suprematist works include Black Square (1915) and White on White (1918).

Malevich exhibited his first Black Square, now at the Tretyakov Gallery in Moscow, at the Last Futurist Exhibition 0,10 in Petrograd (St. Petersburg) in 1915.

He taught at the Vitebsk Practical Art School in Belarus (1919–1922) alongside Marc Chagall, the Leningrad Academy of Arts (1922–1927), the Kyiv State Art Institute (1927–1929), and the House of the Arts in Leningrad (1930). He wrote the book The World as Non-Objectivity, which was published in Munich in 1926 and translated into English in 1959. In it, he outlines his Suprematist theories.

Alfred H. Barr Jr. included several paintings in the groundbreaking exhibition “Cubism and Abstract Art” at the Museum of Modern Art in New York in 1936. In 1939, the Museum of Non-Objective Painting opened in New York, whose founder, Solomon R. Guggenheim - an early and passionate collector of the avant-garde—was inspired by the same aesthetic ideals and spiritual quest that exemplified Malevich’s art.

The first U.S. retrospective of Malevich’s work in 1973 at the Solomon R. Guggenheim Museum provoked a flood of interest and further intensified his impact on postwar American and European artists. In 1989, the Stedelijk Museum in Amsterdam held the West’s first large-scale Malevich retrospective, including the paintings they owned and works from the collection of Russian art critic Nikolai Khardzhiev.

Malevich’s works are held in several major art museums, including the State Tretyakov Gallery in Moscow, and in New York, the Museum of Modern Art, and the Guggenheim Museum. The Stedelijk Museum in Amsterdam owns 24 Malevich paintings, more than any other museum outside of Russia. Another major collection of Malevich works is held by the State Museum of Contemporary Art in Thessaloniki.