  We develop a mean-field theory of the spatial profile and the spectral
properties of polariton condensates in nonresonantly pumped semiconductor
microcavities in the strong coupling regime. Predictions are obtained for both
the continuous-wave and the pulsed excitation regimes and the specific
signatures of the non-equilibrium character of the condensation process are
pointed out. A striking sensitivity of the condensate shape on the optical pump
spot size is demonstrated by analytical and numerical calculations, in good
quantitative agreement with recent experimental observations.
