A review is given of the laws of non-linear optical reflection which govern the direction, polarization and intensity of second harmonic light generated in reflection. The complex non-linear susceptibility of III-V and II-VI piezoelectric compounds has been measured over a range of frequencies and shows characteristic dispersive properties. Both the amplitude and the phase can be determined. When the medium has a centre of inversion, the reflected second harmonic production is several orders of magnitude smaller. The effect has magnetic dipole and electric quadrupole character and has been observed in silicon, germanium and several metals and alloys. In metals the contribution from core electrons and the conduction electron plasma have the same order of magnitude.