The theory of nuclear quadrupole spin–lattice relaxation in anharmonic crystals is developed, both in terms of ordinary perturbation theory and in terms of phonon Green functions. The important relaxation processes are shown to be the direct, first-order Raman, and anharmonic Raman (aR) processes. The aR process is a second-order process due to a combination of the linear spin–lattice coupling and the cubic anharmonic lattice forces, and can be interpreted as arising from the second-order self-energy term in the single-phonon Green function. The effect on the relaxation of the higher-order phonon self-energy and lifetime effects is investigated and shown to be of minor importance. A new method of treating polarization mixing in the Dyson equation for the phonon Green functions is presented. The theory is applied to nuclear quadrupole relaxation in alkali halide crystals and the aR process is shown to be dominant. Nuclear electric dipole and electron paramagnetic relaxation are also discussed.