  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.
