We will discuss methods of computing instanton partition functions for arbitrary gauge groups including the exceptional ones. Even though there is no explicit algebraic construction of instanton moduli space available for the EFG groups beyond 1-instanton, we're able to evaluate the partition function using the blow-up recursion relations derived by Nakajima and Yoshioka. We compare this result with the recent proposal based on the superconformal index of SCFTs with E6, E7 global symmetry. We also compare our result with the norm of certain coherent states of W-algebras and thereby extending the AGT correspondence for pure YM theory to all gauge groups. Reference: 1111.5624, 1205.4722.