Stationary reflection and the singular cardinals hypothesis.

We examine reflection of stationary sets at successors of singular cardinals and its connection with cardinal arithmetic.  For instance it has been open whether the failure of the singular cardinal hypothesis at a singular cardinal mu of uncountable cofinality implies the existence of a nonreflecting stationary subset of mu^+.  In recent joint work with Omer Ben-Neria and Yair Hayut we have shown that the answer is no modulo the consistency of some large cardinals.  In this talk, we survey some instances of methods used in the proof.  In particular, we show how to construct Prikry sequences over iterated ultrapowers and exploit them for combinatorial proofs.