Supersymmetric AdS backgrounds in string and M-theory

We first present a short review of general supersymmetric compactifications in string and M-theory using the language of G-structures and intrinsic torsion. We then summarize recent work on the generic conditions for supersynimetric AdS(5) backgrounds in M-theory and the construction of classes of new solutions. Turning to AdS(5) compactifications in type IIB, we summarize the construction of an infinite class of new Sasaki-Einstein manifolds in dimension 2k + 3 given a positive curvature Kahler-Einstein base manifold in dimension 2k. For k = 1 these describe new supergravity duals for X = 1 superconformal field theories with both rational and irrational R-charges and central charge. We also present a generalization of this construction, that has not appeared elsewhere in the literature, to the case where the base is a product of Kdhler-Einstein manifolds.