We study the geometry and the cohomology of a certain class of (PEL) type Shimura varieties. These varieties arises as moduli spaces of polarized abelian varieties, endowed with an action of a division algebra and a level structure. A conjecture of Langlands describes the l-adic cohomology groups of the Shimura varieties. Following the work of Harris-Taylor (on the local Langlands conjecture), we define the notion of Igusa varieties in this context. Then, combining this approach with the one of Rapoport-Zink (on the p-adic uniformization of Shimura varieties), we describe the geometry of the reduction in positive characteristic of the Shimura varieties. As a result of this analysis, we obtain a description of the l-adic cohomology of the Shimura varieties, in terms of the l-adic cohomologies with compact supports of the Igusa varieties and of the Rapoport-Zink spaces.