Let G be a finite subgroup of SL(2, C) and let X be a
"nice" resolution of singularities of the singular space C^2/G. The classical McKay correspondence gives a bijection between the irreducible representations of G and the components of exceptional divisor in X (which give a basis of its second homology).

We explain how this correspondence follows from a more general statement on categories of sheaves, and give an overview of known generalizations to subgroups of SL(n, C)