We reviewed the literature on the role of working memory in the solution of arithmetic problems such as 3 + 4 or 345 + 29. The literature was neither comprehensive nor systematic, but a few conclusions are tenable. First, all three components of the working memory system proposed by Baddeley (i.e., central executive, phonological loop, and visual‐spatial sketchpad) play a role in mental arithmetic, albeit under different conditions. Second, mental arithmetic requires central executive resources, even for single‐digit problems. Third, further progress in understanding the role of working memory in arithmetic requires that researchers systematically manipulate factors such as presentation conditions (e.g., operand duration, format), problem complexity, task requirements (e.g., verification vs production), and response requirements (e.g., spoken vs written); and that they consider individual differences in solution procedures. Fourth, the encoding‐complex model (Campbell, 1994) seems more likely to account for the variability observed in arithmetic solutions than other models of numerical processing. Finally, working memory researchers are urged to use mental arithmetic as a primary task because the results of the present review suggest that solution of problems that involve multiple digits are likely to involve an interaction of all the components of the working memory system.