Anisimov received a degree in petroleum engineering from Grozny Petroleum Institute in 1964, a doctorate in physical chemistry from Moscow State University in 1969, and a doctor of science degree in molecular and thermal physics from the Kurchatov Institute of Atomic Energy in Moscow in 1976.

From 1969 through 1977, Anisimov worked at the U.S.S.R. State Committee for Standards and Product Quality Management (Russian: Госстандарт), where his postdoctoral mentor was Alexander V.

[1][2] From 1978 until 1993, Anisimov was a professor and the chairman of the physics department of Gubkin Russian State University of Oil and Gas.

In 1994, Anisimov began working in the United States as a professor for both the department of chemical and biomolecular engineering and for the Institute of Physical Science and Technology at the University of Maryland, College Park.

His research group at the University of Maryland (jointly with Jan V. Sengers [2][4]) is one of the leading international authorities in the field of critical phenomena and phase transitions.