Vortices are objects analogous to pseudoholomorphic curves in a version of Gromov-Witten theory adapted to Hamiltonian target spaces; they also describe stable field configurations in gauged sigma models. It is interesting to study their moduli spaces, which come equipped with Kähler metrics encoding physical information on the underlying classical and quantum field theories -- e.g. on the spectrum of quantum ground states, or phase transitions. My talk will focus on the case of models whose targets are Kähler toric manifolds. Recent results about the topology of these moduli spaces and the asymptotics of their metrics will be illustrated in the easiest examples. Some physical implications will also be discussed. I will assume very little background from the audience, apart from the rudiments of toric geometry.