In this report we sketch some of the insights and consequences of
recent work by Andrei Suslin and Vladimir Voevodsky concerning
algebraic K-theory and motivic cohomology. We can trace these
developments to a lecture at Luminy by Suslin in 1987
and to Voevodsky's Harvard thesis in 1992. What results is a powerful
general theory of sheaves with transfers on schemes over a field, a
theory developed primarily by Voevodsky with impressive applications
by Suslin and Voevodsky.
This paper was delivered at Seminar Bourbaki.