  An important class of `physically relevant' measures for dynamical systems
with hyperbolic behavior is given by Sinai-Ruelle-Bowen (SRB) measures. We
survey various techniques for constructing SRB measures and studying their
properties, paying special attention to the geometric `push-forward' approach.
After describing this approach in the uniformly hyperbolic setting, we review
recent work that extends it to non-uniformly hyperbolic systems.
