Nekrasov instanton functions were originally defined as partition functions in a 4D gauge theory (they can be also treated as generating functions for intersection numbers of homology classes on the moduli spaces of instantons). It turns out that these function appear in several apparently unrelated subjects of mathematical physics. In particular they can be defined in purely 2D terms of conformal field theory. In the simplest cases this goes back to the fermionic representations of tau-functions. The AGT conjecture relates Nekrasov functions (for N=2 supersymmetric Yang-Mills theories) to the highest weight Virasoro modules. We shall discuss also the relation of this approach to the Seiberg-Witten curves, prepotentials and Belavin-Polyakov-Zamolodchikov equations.