I present recent results on particle production during the reheating after inflation. We focus on the late-time evolution of the scalar inflationary field, during its coherent oscillation regime. We specifically consider the production of dark matter and radiation, restricting our attention to gravitational interactions, including minimal and non-minimal coupling to gravity. We also consider leptogenesis through the gravitational production of heavy right-handed neutrinos during reheating. Interesting constraints from primordial gravitational wave measurements are derived within this scenario.