We review our study of Sasakian geometry as an agent for proving the
existence of Einstein metrics on odd dimensional manifolds. Particular emphasis
is given to the Sasakian structures occuring on links of isolated hypersurface
singularities.Comment: This is an expository article that grew out of notes for the three
lectures the second author presented during the XXIV-th Winter School of {\it
Geometry and Physics} in Srni, Czech Republic, in January of 2004., 30 pages.
Some new examples and references were adde