We will give an introduction to various versions of the crepant resolution conjecture. This is a whole collection of theorems and conjectures which relate the geometry of a Calabi-Yau orbifold to the geometry of a crepant resolution. It includes the classical and derived McKay correspondences, Ruan's cohomological crepant resolution conjecture, and various versions of the Gromov-Witten and Donaldson-Thomas crepant resolution conjectures.