Landau, whose father was a petroleum engineer and whose mother was a physician, was born in Baku, the capital of Azerbaijan. He studied at the university in his native city (1922–24) and at Leningrad (now St. Petersburg) (1924–27), graduating in 1927. In 1929 he visited various scientific centers in Europe, including Copenhagen where he developed a long-lasting friendship and working relationship with Niels Bohr. He returned to the Soviet Union and in 1932 went from Leningrad to Kharkov to head the theoretical physics groups at two of the institutes there. He was appointed professor of physics at Kharkov University in 1935. In 1937, at the request of Pyotr Kapitza, he moved to Moscow as director of theoretical physics at the Institute of Physical Problems and in 1943 became professor of physics at the Moscow State University.

Landau was one of the major theoretical physicists of his day, making numerous contributions to many branches of physics. These included quantum mechanics, atomic and nuclear physics, astrophysics, thermodynamics, particle physics, quantum electrodynamics, and low-temperature physics. In Moscow he collaborated with E. M. Lifshitz on a highly successful series of monographs on theoretical physics, published in 1938. In 1962 he was awarded the Nobel Prize for physics for his work on condensed matter (i.e., matter in the solid or liquid state), especially liquid helium. Liquid helium has such unusual properties when its temperature falls below 2.2 kelvin that physicists describe it as helium II, as opposed to helium I above 2.2 K. To explain the strange superfluidity and superconductivity of helium II, Landau introduced the idea of a ‘phonon’, a quantum of thermal energy, and a ‘roton’, an elementary quantum of vortex motion. The existence of such entities has since been confirmed experimentally.

Under Landau a vigorous school of theoretical physics was created in Moscow. Tragically he was involved in a serious motor accident in 1962 and although strenuous efforts were made to keep him alive his physical powers never returned to normal and he died six years later.