  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
supersymmetric 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 N=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
Kahler-Einstein manifolds.
