The study of learning and memory is a research area that has been driven by models since at least the 1940's. Over the years, the emphasis in mathematical modelling has shifted from very precise fitting of single experiments to what might be best described as semi-quantitative fitting of a wide variety of phenomena from a number of experimental paradigms (compare for instance Bower's one-element model [Bower, 1961] to any of the current models such as ACT* [Anderson, 1983b], SAM [Raaijmakers & Shiffrin, 1981; Gillund & Shiffrin, 1984] or TODAM [Murdock, 1982]).
The complexities of recent models contributes to the apparent impossibility of deciding between them. Although couched in quite different terms, they often make very similar predictions, at least under appropriate choices of parameters. This makes it difficult to generate critical empirical tests. On the other hand, the similarity of predictions suggests real progress in theory development, forced by the necessity to account for a standard and agreed upon corpus of findings.
In this chapter, we will review a number of the most important contemporary models of memory, trying to highlight the similarities and differences in the way they handle basic facts about recall and recognition. Space limitations prevent us from any attempt at exhaustive coverage. For the same reason, although a number of models can or do predict response latencies, we leave coverage of this important topic to a future chapter.