  We study, analytically and with lattice simulations, the decay of coherent
field oscillations and the subsequent thermalization of the resulting
stochastic classical wave-field. The problem of reheating of the Universe after
inflation constitutes our prime motivation and application of the results. We
identify three different stages of these processes. During the initial stage of
``parametric resonance'', only a small fraction of the initial inflaton energy
is transferred to fluctuations in the physically relevant case of sufficiently
large couplings. A major fraction is transfered in the prompt regime of driven
turbulence. The subsequent long stage of thermalization classifies as free
turbulence. During the turbulent stages, the evolution of particle distribution
functions is self-similar. We show that wave kinetic theory successfully
describes the late stages of our lattice calculation. Our analytical results
are general and give estimates of reheating time and temperature in terms of
coupling constants and initial inflaton amplitude.
