Abstract. I will explain how to compute the Hilbert series that counts chiral operators parametrising the Coulomb branch of the moduli space of vacua of three-dimensional N=4 supersymmetric gauge theories. The formalism has applications to Physics, such as to the study of infrared dualities in three dimensions and of string backgrounds with eight supercharges, as well as to Mathematics, where it provides a new construction of HyperKaehler cones as algebraic varieties. I will then show how the Coulomb branch of certain 3d N=4 generalised quiver gauge theories can be used to compute the Hilbert series of the moduli space of k G-instantons, for any simple Lie group G. The construction is alternative to the ADHM construction that is only available for classical groups G.