We use Darwin's theory (Darwin, 1880) to derive the main results on the orbital and rotational evolution of a close-in companion (exoplanet or planetary satellite) due to tidal friction. The given results do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tide harmonics (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the study of the synchronization of the planetary rotation in the two possible final states for a non-zero eccentricity : (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) the capture into a 1:1 spin-orbit resonance (true synchronization), which is only possible if an additional torque exists acting in opposition to the tidal torque. Results are given under the assumption that this additional torque is produced by a non-tidal permanent equatorial asymmetry of the planet. The indirect tidal effects and some non-tidal effects due to that asymmetry are considered. For sake of comparison with other works, the results obtained when tidal lags are assumed proportional to the corresponding tidal wave frequencies are also given.