I will review a deep correspondence between N=2 superconformal field theories in four dimensions and vertex operator algebras. Recent work with L. Rastelli has identified the Higgs branch of a four-dimensional SCFT with a geometric invariant of the corresponding VOA: the ¡°associated variety¡±. This connection implies surprising modularity properties for the superconformal index of the four-dimensional theory, and also hints at the possibility of reconstructing the VOA from moduli space data.