In this chapter, we attempt first to describe the different emphases inherent in traditional experimental and individual differences approaches. Next, we discuss the types of cognitive models that have been proposed to account for mental arithmetic performance. In doing so, the nature of the basic theoretical propositions (e.g., underlying the retrieval of answers from a memory store) and the proper means of testing these propositions will be stressed. Then, we survey the findings of several studies, highlighting recently published findings on individual and developmental differences in the skills underlying proficiency in mental addition. One unique contribution of an individual differences approach is the external validation of proposed models specifying the elementary cognitive processes invoked during problem solution. External validation requires the fitting of statistical models to data from each individual, resulting in the estimation of parameters that reflect speed of executing each of various cognitive processes, or elementary cognitive components. Then, individual differences in these parameter estimates, or component scores, are related to individual differences on traditional measures of ability and achievement. Various implications of our findings for research on numerical facility and for applications in education are also discussed.