3d supersymmetric gauge theories and Hilbert series

The Hilbert series is a generating function that enumerates gauge invariant chiral operators of a supersymmetric field theory with four supercharges and an R-symmetry. In this article I review how counting dressed 't Hooft monopole operators leads to a formula for the Hilbert series of a 3d N >= 2 gauge theory, which captures precious information about the chiral ring and the moduli space of supersymmetric vacua of the theory. (Conference paper based on a talk given at String-Math 2016, College de France, Paris.)