The mechanisms involved in the formation of impact craters are examined theoretically, reviewing the results of recent investigations. Topics addressed include crater morphology, stress waves in solids, the contact and compression stage, the excavation stage, and ejecta deposits. Consideration is given to the scaling of crater dimensions, the crater modification stage, multiring basins, cratered landscapes, atmospheric interactions, and the implications of impact cratering for planetary evolution. Extensive diagrams, graphs, tables, and images of typical craters are provided.