When an intense femtosecond laser pulse hits an optically-polished surface, it generates a dense plasma that itself acts as a mirror, known as a plasma mirror. As this mirror reflects the highintensity laser field, its non-linear temporal response can lead to a periodic temporal distortion of the reflected wave, associated to a train of attosecond light pulses, and, in the frequency domain, to the generation of high-order harmonics of the laser. This paper presents detailed theoretical and numerical analysis of the two dominant harmonic generation mechanisms identified so far, Coherent Wake Emission and the Relativistic Oscillating Mirror. Parametric studies of the emission efficiency are presented in these two regimes, and the phase properties of the corresponding harmonics are discussed. This theoretical study is complemented by a synthesis of recent experimental results, which establishes that these two mechanisms indeed dominate harmonic generation on plasma mirrors.