Ion bombardment of insulating surfaces such as Al(2)O(3) and SiO(2) produces ordered patterns of ripples. The ripple wavelength varies with ion energy, incidence angle and substrate temperature. A region of stability is also known to exist for near-normal incidence during Ar(+) ion bombardment, where initially rough surfaces are smoothened. A number of relaxation mechanisms are found to be operative under specific conditions, including: surface-confined viscous flow, impact-induced lateral currents and impact-assisted surface diffusion during ion bombardment at high temperatures. Most of the experimentally observed phenomena are explained through extension of the Bradley-Harper theory by the addition of these new processes. Phenomena that are not explained by the linear theory, such as the saturation of surface amplitude during the formation of ripples, are thought to arise from nonlinear effects. This contribution describes the present status of the linear theory relevant to this class of materials and recent experimental results.