His work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology led to the award of a Fields Medal in 2002.

[1] He received his Ph.D. in mathematics from Harvard University in 1992 after being recommended without even applying and without a formal college degree, following several independent publications;[1] he was advised there by David Kazhdan.

While he was a first year undergraduate, he was given a copy of "Esquisse d'un Programme" (submitted a few months earlier by Alexander Grothendieck to CNRS) by his advisor George Shabat.

In January 2009, at an anniversary conference in honor of Alexander Grothendieck, held at the Institut des Hautes Études Scientifiques, Voevodsky announced a proof of the full Bloch–Kato conjectures.

This led to important advances in type theory and in the development of new univalent foundations of mathematics that Voevodsky worked on in his final years.