Quantum field theories in (2+1)-dimensions exhibit a beautiful property known as particle-vortex duality. It relates, in a precise way, two different excitations on the plane, the familiar particle-like excitations that arise from quantisation of the field and vortices, solitonic-excitations defined by the winding of a local order parameter. Originally studied in the context of anyonic superconductivity and Neilsen-Olesen vortices, extensions of the duality have recently found application to, for example, topological quantum matter. I will review some of these developments and show how recent progress in understanding non-abelian T-duality can be used to define a non-abelian particle-vortex duality in (2+1)-dimensions.