His broad field of work included the theory of superconductivity and superfluidity, quantum electrodynamics, nuclear physics and particle physics. In 1937 he became head of the theory department of the Institute for Physical Problems in the former Soviet Union; he was also a member of the Academy of Sciences. Arrested under the rule of Stalin and Berija in 1938, but released one year later.
He was a Nobel Laureate in Physics for the year 1962 for his pioneering theories of condensed matter, especially liquid helium. He is also admired for a prolific series of textbooks on theoretical physics, co-authored with E.M. Lifshitz.
He died in Moscow.