We review and augment our recent work which demonstrates that a surface layer of altered composition can have a crucial effect on pattern formation induced by ion bombardment of a solid surface. First, we discuss a theory that explains the genesis of the strikingly regular hexagonal arrays of nanodots that can form when the binary material GaSb is bombarded at normal incidence. In the theory, the coupling between a surface layer of altered stoichiometry and the topography of the surface is the key to the observed pattern formation. For a certain range of the parameters, we find that nanodot arrays with strong short-range hexagonal order emerge spontaneously. Well-ordered arrays of nanoholes develop in another range of the parameters. A closely related theory governs the dynamics of the surface of an elemental material that is seeded with impurities during ion bombardment. If the incident impurity flux exceeds a critical value, the surface layer in which impurities are present destabilizes the surface, leading to the formation of a disordered array of nanodots. (C) 2011 Elsevier B. V. All rights reserved.