Cognitive control has long been one of the most active areas of computational modeling work in cognitive science. The focus on computational models as a medium for specifying and developing theory predates the PDP books, and cognitive control was not one of the areas on which they focused. However, the framework they provided has injected work on cognitive control with new energy and new ideas. On the occasion of the books' anniversary, we review computational modeling in the study of cognitive (...) control, with a focus on the influence that the PDP approach has brought to bear in this area. Rather than providing a comprehensive review, we offer a framework for thinking about past and future modeling efforts in this domain. We define control in terms of the optimal parameterization of task processing. From this vantage point, the development of control systems in the brain can be seen as responding to the structure of naturalistic tasks, through the filter of the brain systems with which control directly interfaces. This perspective lays open a set of fascinating but difficult research questions, which together define an important frontier for future computational research. (shrink)