Vertex algebras have deep connections to moduli spaces and enumerative geometry. Affine vertex algebras are closely related to the Verlinde formula for Bun_G, while affine W-algebras play a central role in the AGT conjecture, describing the cohomology of moduli spaces of G-instantons. More recently, Joyce has shown that lattice vertex algebras arise naturally in enumerative geometry, particularly in the study of wall-crossing formulas. In this talk, I will explain how Joyce’s vertex algebras also lead to Virasoro constraints for moduli spaces of sheaves.