This chapter concerns symbolic problem-solving skills and discusses differences in memory use by experts and novices in a number of problem domains, including chess, physics, mathematics, computer programming, map reading and political science. Early studies of chess skill supported a pattern-recognition model of chess expertise. This model accounted for the observed superiority in recall for realistic chess position by experts and the lack of difference in recall for randomised positions between experts and novices. Further, the model suggested that move-choosing skill reflected superior pattern recognition coupled with appropriate actions in a production-system type of organisation. More recent studies of chess skill, however, suggest strongly that the pattern recognition model is over-simple; players at the same skill level can vary in efficiency of pattern encoding and more skilled players choose better moves even when no familiar patterns are present. Current research on chess skill stresses the role of mental search, position-evaluation and general knowledge of chess strategy and tactics. Chess inspired pattern-recognition models have been developed for many of the other fields reviewed here and have been successful in the analyses so far reported. However, given the re-examination of the role of search in chess skill, we argue that studies of expertise in non-adversary domains might benefit from a similar re-evaluation of search-based explanations. It is surmised that more complex models than those currently in use will ultimately be required for all areas of expertise.