From 1921 to 1927 he was a student at Vkhutemas, where he wrote satirical poems and comic plays, including collaborations with Viktor Ardov, Ilya Ilf, Yevgeny Petrov, Valentin Kataev, Vladimir Mass, and Nikolai Erdman.

By January 1942, as a result of Erdman's connections to Lavrenty Beria, they obtained a transfer to Moscow, where they were assigned to write patriotic material for the Song and Dance Ensemble at the Central Club of the NKVD.

From 1948 to 1971, Volpin produced scripts and lyrics to the animation studio Soyuzmultfilm, notably The Enchanted Boy, The Story of a Crime, It Was I Who Drew the Little Man, and The Key.

In 1950, they were awarded the Stalin Prize for their work on Brave People, along with director Konstantin Yudin, cinematographer Igor Geleyn, and actors Sergei Gurzo and Aleksei Gribov.

More familiar to contemporary audiences[2] are Volpin's contributions to the fantasy genre: Jack Frost and Fire, Water, and Brass Pipes, both directed by Aleksandr Rou.