  Vladimir Voevodsky was born in 1966. He studied at Moscow State University
and Harvard university. He is now Professor at the Institute for Advanced Study
in Princeton.
  Among his main achievements are the following: he defined and developed
motivic cohomology and the ${\mathbf A}^1$-homotopy theory of algebraic
varieties; he proved the Milnor conjectures on the $K$-theory of fields. This
article is a brief introduction to this work, for which Voevodsky was awarded
the Fields Medal.
