The theory of reheating of the Universe after inflation is developed. The transition from inflation to the hot Universe turns out to be strongly model-dependent and typically consists of several stages. Immediately after inflation the field \(\phi\) begins rapidly rolling towards the minimum of its effective potential. Contrary to some earlier expectations, particle production during this stage does not lead to the appearance of an extra friction term \(\Gamma\dot\phi\) in the equation of motion of the field \(\phi\). Reheating becomes efficient only at the next stage, when the field \(\phi\) rapidly oscillates near the minimum of its effective potential. We have found that typically in the beginning of this stage the classical inflaton field \(\phi\) very rapidly (explosively) decays into \(\phi\)-particles or into other bosons due to broad parametric resonance. This stage cannot be described by the standard elementary approach to reheating based on perturbation theory. The bosons produced at this stage, as well as some part of the classical field \(\phi\) which survives the stage of explosive reheating, should further decay into other particles, which eventually become thermalized. The last stages of decay can be described in terms of perturbation theory. Complete reheating is possible only in those theories where a single massive \(\phi\)-particle can decay into other particles. This imposes strong constraints on the structure of inflationary models. On the other hand, this means that a scalar field can be a cold dark matter candidate even if it is strongly coupled to other fields.
