Every N=2 SCFT in four dimensions comes equipped with a vertex operator algebrathat encodes the spectrum

and OPE coefficients of an infinite class of 1/4 BPS operators knownas Schur operators. I will discuss a number

of results as well as open questions regarding thestructural properties of the VOAs that appear in this

correspondence and their relationship to four-dimensional physics. I will discuss a proposal for how to recover of

the Higgs branch ofvacua from the VOA and the consequences of this proposal for the behaviour of Schur superconformal

indices under modular transformations. This leads to a surprising relationship between the a-type Weyl

anomaly coefficient and the spectrum of surface operators in an N=2 SCFT.