I will explain the construction of Galois representations associated with conjugate self-dual cuspidal automorphic representations of GL(n) over a CM field which are regular and algebraic, building upon the work of Kottwitz, Clozel and Harris-Taylor (under a mild assumption when n is even). The basic approach is to realize the Galois representations in the cohomology of certain compact Shimura varieties for U(1,n-1) if n is odd and U(1,n) if n is even. For the latter one has to understand the endoscopic part of the cohomology, which was envisioned by Langlands and studied by Blasius and Rogawski in the case of U(1,2). To describe the Galois reprsentations at ramified places, one needs inputs from the study of bad reduction of Shimura varieties (to be explained in the lectures by Fargues and Mantovan).