We give some geometric conditions which are necessary and sufficient for the existence of Sinai-Ruelle-Bowen (SRB) measures for
C^{1+\alpha} surface diffeomorphisms.   As part of our argument we give an original method for constructing first return Young Towers,
which demonstrates that every hyperbolic measure, and in particular every SRB measure,  can be lifted to such a tower. This method relies
on a new result in non-ununiform hyperbolicity theory which is independent of interest. Joint work with V. Climenhaga and Y. Pesin.