We will review our current understanding of reheating after inflation, including various aspects of the linear and nonlinear dynamics of the inflaton field, such as parametric resonance, the generation of metric perturbations and the effects of the nonlinear evolution on the post-inflationary expansion history. We will also review the recent progress in the understanding of the non-perturbative dynamics of vector fields during reheating. Finally, we will discuss phenomenologically interesting models of gauge fields during inflation which can give rise to detectable gravitational wave signatures.