Research on the structures and processes involved in simple mental arithmetic is reviewed. Results suggest that mental arithmetic is a memory retrieval phenomenon, which develops with the experiences of elementary school and can be understood in general as retrieval from organized network representations. Simple mental addition with basic facts was examined in children from grades 1 and 5 and in college students. The data indicate that two models are necessary to describe the development of addition performance. These models are a simple counting framework for children in the early stages of mastery, followed by the network retrieval model from about the fourth or fifth grade on. The most basic result in studies of mental arithmetic is the problem size effect--a regular increase in reaction time (RT) as the numerical size of the problem increases. The RT performance varies with task (verbal production vs. verification), problem size, and age. The report recommends use of the true/false verification task in future studies of the psychology of arithmetic performance, as data generated from such tasks is more amenable to information processing models. (MP)