A concise summary of out-of-equilibrium dark matter production during post-inflationary reheating is presented. We show that the dark matter relic abundance is in general sensitive to the thermalization rate of the inflaton decay products, and the evolution of the temperature of the subsequently thermalized radiation. We discuss how smoking-gun signals, such as monochromatic neutrinos or gamma-ray lines, or Lyman-$\alpha$ data, can help constrain out-of-equilibrium DM models.