Developments in supergravity, superstrings and M-theory imply that the study of higher-dimensional black holes is a topic of considerable importance, especially with regard to the AdS/CFT Correspondence. In this talk, we present recent results on the construction of rotating black holes in anti-de Sitter backgrounds and in gauged supergravities. The higher-dimensional Kerr-AdS black holes exhibit remarkable symmetry properties analogous to those of four dimensions, and which lead to the construction of more general Kerr-NUT-AdS metrics. By considering supersymmetric limits we can obtain large families of non-singular Einstein-Sasaki spaces, and also metrics describing smooth resolutions of cones over Einstein-Sasaki spaces.