We derive a theory of polariton Bose-Einstein condensation based on the many-body quantum field theory of interacting Bose particles. In particular, we describe self-consistently the linear exciton-photon coupling and the exciton-non-linearities, by generalizing the Hartree-Fock-Popov description of BEC to the case of two coupled Bose fields at thermal equilibrium. In this way, we compute the density-dependent one-particle spectrum, the energy occupations and the phase diagram. The results quantitatively agree with the existing experimental findings. We discuss the conditions under which polaritons can be considered as a dilute Bose gas at thermal equilibrium. While the diluteness is enforced by the very peculiar energy-momentum dispersion, thermal equilibrium is only partially achieved in common experiments. A basic tool to model the kinetics of polariton BEC is then derived in terms of Boltzmann equations, including polariton-phonon and polariton-polariton scattering. We discuss under which conditions thermal equilibrium condensation can be reached and how to design future microcavity samples in order to reach this goal.