  In this talk recent developments of the theory of preheating after inflation
are briefly reviewed. In inflationary cosmology, the particles constituting the
Universe are created after inflation due to their interaction with moving
inflaton field(s) in the process of reheating. In inflationary models motivated
by supergravity, both bosons and fermions are created. In the bosonic sector,
the leading channel of particle production is the non-perturbative regime of
parametric resonance dominated by those bosons which are created exponentially
fast with the largest characteristic exponent. In the fermionic sector, the
leading channel corresponds to the regime of parametric excitation of fermions,
which respects Pauli blocking but differs significantly from the perturbative
expectation. In supergravity we also have to consider production of gravitinos
and moduli fields, which are cosmologically dangerous relics. We discuss the
derivation of the gravitino equations in curved space-time with moving
background scalars. We describe recent results on the production of gravitinos
from preheating, which may put strong constraints on the inflationary models.
