Mathematical models of memory are useful for describing basic processes of memory in a way that enables generalization across a number of experimental paradigms. Models that have these characteristics do not just engage in empirical curve-fitting, but may also provide explanations for puzzling phenomena and may lead to new discoveries. This chapter provides a number of examples, taken from previous research with the SAM model. Although previous research has focused exclusively on the explanation of episodic memory, recent research within the SAM/REM approach has extended this model to implicit and semantic memory phenomena. This review provides some speculations on how this approach may be extended to deal with a number of basic data in implicit memory. It is emphasized that constructing a model for implicit memory necessitates the development of detailed models of lexical-semantic processing.