This article summarizes theoretical work on sputtering during the past decade, with the emphasis on elemental sputtering in the linear cascade and spike regimes as well as alloy sputtering. The sputtering of molecules and clusters, and electronic sputtering of insulators and biomolecular materials are discussed more briefly, and topics like charge and excitation states of sputtered particles as well as surface topography are left out, in view of contemporary summary papers in this issue and elsewhere. The paper is nontutorial and assumes some general knowledge of the field on the part of the reader, based e.g. on ref.  or ref. . The discussion emphasizes principles and methods as well as open problems rather than quantitative results. A few general recommendations for efficient utilization of computer simulation conclude the paper.