Tremendous progress in the science of extrasolar planets has been achieved since the discovery of a Jupiter orbiting the nearby Sun-like star 51 Pegasi in 1995. Theoretical models have now reached enough maturity to predict the characteristic properties of these new worlds, mass, radius, atmospheric signatures, and can be confronted with available observations. We review our current knowledge of the physical properties of exoplanets, internal structure and composition, atmospheric signatures, including expected biosignatures for exo-Earth planets, evolution, and the impact of tidal interaction and stellar irradiation on these properties for the short-period planets. We discuss the most recent theoretical achievements in the field and the still pending questions. We critically analyze the different solutions suggested to explain abnormally large radii of a significant fraction of transiting exoplanets. Special attention is devoted to the recently discovered transiting objects in the overlapping mass range between massive planets and low-mass brown dwarfs, stressing the ambiguous nature of these bodies, and we discuss the possible observable diagnostics to identify these two distinct populations. We also review our present understanding of planet formation and critically examine the different suggested formation mechanisms. We expect this review will provide the basic theoretical background to capture the essentials of the physics of exoplanet formation, structure and evolution and the related observable signatures.