Aspects of the McKay correspondence

We start with the 2-dimensional case: for G a finite subgroup of SL_2(C) we recall the relation with the Dynkin diagrams, the representations of G, the Hilbert scheme of G-orbits. We state some open questions related to this topic, such as crepant resolution versus minimal resolution, the derived conjecture, etc. We survey some of the known cases: symplectic
case, Craw-Reid algorithm, some examples and counterexamples in high dimension (combining results of Bridgeland-King-Reid and Nakamura).