The operation of different brain systems involved in different types of memory is described. One is a system in the primate orbitofrontal cortex and amygdala involved in representing rewards and punishers, and in learning stimulus-reinforcer associations. This system is involved in emotion and motivation. A second system in the temporal cortical visual areas is involved in learning invariant representations of objects. A third system in the hippocampus is implicated in episodic memory and in spatial function. Fourth, brain systems in the frontal and temporal cortices involved in short term memory are described. The approach taken provides insight into the neuronal operations that take place in each of these brain systems, and has the aim of leading to quantitative biologically plausible neuronal network models of how each of these memory systems actually operates.