In the first part of the talk I will describe the vortex equations and some of its simplest moduli space of solutions. In the second part I will describe the natural $L^2$-metric on these moduli spaces and explain how, in certain cases, one can explicitly compute its Kahler class and total volume. As a by-product this leads to conjectural formulae for the volume of the space of holomorphic maps of fixed degree from a compact Riemann surface to projective space.