When his father took a post advising the Soviet government, the family moved to Moscow. Life there became difficult, and his father secured permission from Lenin and the Politburo to take his son to London in 1921.
Young Liberman was educated in Russia, England, and France, where he took up life as a "White Émigré" in Paris.
He began his publishing career in Paris with the early pictorial magazine Vu, where he worked under Lucien Vogel and with photographers such as Brassaï, André Kertész, and Robert Capa.
After emigrating to New York in 1941, he began working for Condé Nast Publications, rising to the position of editorial director, which he held from 1962-1994.
Only in the 1950s did Liberman take up painting and, later, metal sculpture. His highly recognizable sculptures are assembled from industrial objects (segments of steel I-beams, pipes, drums, and such), often painted in uniform bright colors. In a 1986 interview concerning his formative years as a sculptor and his aesthetic, Liberman said, "I think many works of art are screams, and I identify with screams." Prominent examples of his work are in the collections of the Metropolitan Museum of Art, Storm King Art Center, Hirshhorn Museum and Sculpture Garden, Pyramid Hill Sculpture Park, Tate Gallery, and the Guggenheim Museum. His massive work "The Way", a 65 feet (20 m) x 102 feet (31 m) x 100 feet (30 m) structure, is made of eighteen salvaged steel oil tanks, and became a signature piece of Laumeier Sculpture Park, and a major landmark of St. Louis, Missouri.
He was married briefly to Hildegarde Sturm (August 25, 1936), a model and competitive skier. His second wife (since 1942), Tatiana Yacovleff du Plessix Liberman (1906–1991), had been a childhood playmate and baby sitter. In 1941, they escaped together from occupied France, via Lisbon, to New York. She had operated a hat salon in Paris, then designed hats for Henri Bendel in Manhattan. She continued in millinery at Saks Fifth Avenue where she was billed as "Tatania du Plessix" or "Tatania of Saks", until the mid-1950s. In 1992, he married Melinda Pechangco, a nurse who had cared for Tatiana during an early illness. His stepdaughter, Francine du Plessix Gray, is a noted author.