Given either a moduli space of  sheaves on a smooth projective variety or a moduli space of representations of a quiver, one can obtain enumerative invariants by integrating natural cohomology classes. Such numbers often have interesting structures behind, and I will talk about two: wall-crossing  (how the numbers change when the stability parameter moves) and Virasoro constraints (universal relations among such numbers). Both of these phenomena are best understood in terms of a vertex algebra that D. Joyce defined. I will explain what this vertex algebra is and its role in the proof of Virasoro constraints, focusing for simplicity in the quiver setting.