  We study the quatum to classical transition process in the context of quantum
field theory. Extending the influence functional formalism of Feynman and
Vernon, we study the decoherence process for self-interacting quantum fields in
flat space. We also use this formalism for arbitrary geometries to analyze the
quantum to classical transition in quantum gravity. After summarizing the main
results known for the quantum Brownian motion, we consider a self-interacting
field theory in Minkowski spacetime. We compute a coarse grained effective
action by integrating out the field modes with wavelength shorter than a
critical value. From this effective action we obtain the evolution equation for
the reduced density matrix (master equation). We compute the diffusion
coefficients for this equation and analyze the decoherence induced on the
long-wavelength modes. We generalize the results to the case of a conformally
coupled scalar field in de Sitter spacetime. We show that the decoherence is
effective as long as the critical wavelength is taken to be not shorter than
the Hubble radius. On the other hand, we study the classical limit for
scalar-tensorial models in two dimensions. We consider different couplings
between the dilaton and the scalar field. We discuss the Hawking radiation
process and, from an exact evaluation of the influence functional, we study the
conditions by which decoherence ensures the validity of the semiclassical
approximation in cosmological metrics. Finally we consider four dimensional
models with massive scalar fields, arbitrary coupled to the geometry. We
compute the Einstein-Langevin equations in order to study the effect of the
fluctuations induced by the quantum fields on the classical geometry.
