The lifetime of optical components is determined by the combination of laser-induced damage initiation probability and damage propagation rate during subsequent laser shots. This paper reviews both theoretical and experimental investigations on laser-induced damage initiation and growth at the surface of optics. The damage mechanism is generally considered as thermal absorption and electron avalanche, which play dominant roles for the different laser pulse durations. The typical damage morphology in the surface of components observed in experiments is also closely related to the damage mechanism. The damage crater in thermal absorption process, which can be estimated by thermal diffusion model, is typical distortion, melting, and ablation debris often with an elevated rim caused by melted material flow and resolidification. However, damage initiated by electron avalanche is often accompanied by generation of plasma, crush, and fracture, which can be explained by thermal explosion model. Damage growth at rear surface of components is extremely severe which can be explained by several models, such as fireball growth, impact crater, brittle fracture, and electric field enhancement. All the physical effects are not independent but mutually coupling. Developing theoretical models of multiphysics coupling are an important trend for future theoretical research. Meanwhile, more attention should be paid to integrated analysis both in theory and experiment.