Alexander was born to a privileged family - his father not only managed to keep his place in the society after the Revolution of 1917, but also to become an important advisor to the new Soviet regime. Even more, he secured permission from the Politburo and Lenin himself to send his son to London in 1921.
Young Liberman was educated in France, where he took up life as a "White Émigré" in Paris. It was there where 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 the famous publishing house Condé Nast Publications, rising to the position of editorial director, which he held until 1994. For many years he also was the artistic director of the prominent Vogue magazine, helping the publication greatly to become the de-facto leader of the fashion media it is now.
His personal life was as rich as his creative career: his second wife was Tatiana Yacovleff du Plessix Liberman (1906–1991), the famous Russian-French-American fashion designer and Mayakovsky's former muse and lover, and his stepdaughter was Francine du Plessix Gray, a noted literature critic and a popular author, nominated for the Pulitzer prize.
His escape to America with Tatiana is the subject of urban legends. He and his wife were trapped in Paris by the quickly advancing German troops, and Liberman had to steal and doctor documents allowing them passage to Portugal. From Lisbon they escaped to New York.
Liberman took up art relatively late - only in the 1950s – first starting painting and, later, creating metal sculptures. His highly recognizable sculptures are assembled from industrial objects, painted in uniform bright colors. In his interview about his years as a sculptor, Liberman said, "I think many works of art are screams, and I identify with screams."
His works found his way into the collections of the best museums and exhibitions: Metropolitan Museum of Art, Storm King Art Center, Hirshhorn Museum and Sculpture Garden, Pyramid Hill Sculpture Park, Tate Gallery, and the Guggenheim Museum! And his largest work "The Way", a 20-meter high structure made of 18 steel oil tanks, became a signature landmark of St. Louis, Missouri.
He was married briefly to Hildegarde Sturm (August 25, 1936), a model and competitive skier. After the death of Tatiana Yacovleff du Plessix Liberman in 1991, he married Melinda Pechangco, an old friend and a nurse who had cared for Tatiana during an illness.