He received his bachelor's degree in mathematics from Moscow State University in 1989 and his Ph. D. in mathematics from Harvard University in 1992. Currently he is a full professor at the Institute for Advanced Study in Princeton.
In 2002 at the 24th International Congress of Mathematicians in Beijing, China he received the Fields Medal together with Laurent Lafforgue. Voevodsky made outstanding advances in algebraic geometry.
He is coauthor (with A. Suslin and E.M. Friedlander) of Cycles, Transfers and Motivic Homology Theories (Princeton University Press, 2000).