Research over the past decade has suggested that the ability to hold information in visual working memory (VWM) may be limited to as few as three to four items. However, the precise nature and source of these capacity limits remains hotly debated. Most commonly, capacity limits have been inferred from studies of visual change detection, in which performance declines systematically as a function of the number of items that participants must remember. According to one view, such declines indicate that a limited number of fixed-resolution representations are held in independent memory "slots." Another view suggests that such capacity limits are more apparent than real, but emerge as limited memory resources are distributed across more to-be-remembered items. Here we argue that, although both perspectives have merit and have generated and explained impressive amounts of empirical data, their central focus on the representations--rather than processes--underlying VWM may ultimately limit continuing progress in this area. As an alternative, we describe a neurally grounded, process-based approach to VWM: the dynamic field theory. Simulations demonstrate that this model can account for key aspects of behavioral performance in change detection, in addition to generating novel behavioral predictions that have been confirmed experimentally. Furthermore, we describe extensions of the model to recall tasks, the integration of visual features, cognitive development, individual differences, and functional imaging studies of VWM. We conclude by discussing the importance of grounding psychological concepts in neural dynamics, as a first step toward understanding the link between brain and behavior.