If R is a local Gorenstein ring then a non-commutative crepant resolution for R is a reflexive R-module M such that the endomorphism ring of M is Cohen-Macaulay as an R-module and has finite global dimension. This turns out to be a sensible generalization of the algebraic geometry concept of a crepant resolution of singularities. We will give background on non-commutative resolutions and survey some of the existence / non-existence results.