* Lenin Prize (1959)
* Nobel Prize in Physics (1964, with the pioneering work done in the field of quantum electronics)
* Hero of Socialist Labour — twice (1969, 1982)
* Gold Medal of the Czechoslovak Academy of Sciences (1975)
* A. Volta Gold Medal (1977)
* Kalinga Prize (1986)
* USSR State Prize (1989)
* Lomonosov Grand Gold Medal, Moscow State University (1990)
* Order of Lenin – five times
* Order of Merit for the Fatherland, 2nd class
* Order of the Patriotic War, 2nd class