  We give an expository account of a conjecture, developed by
Coates--Corti--Iritani--Tseng and Ruan, which relates the quantum cohomology of
a Gorenstein orbifold X to the quantum cohomology of a crepant resolution Y of
X. We explore some consequences of this conjecture, showing that it implies
versions of both the Cohomological Crepant Resolution Conjecture and of the
Crepant Resolution Conjectures of Ruan and Bryan--Graber. We also give a
"quantized" version of the conjecture, which determines higher-genus
Gromov--Witten invariants of X from those of Y.
