This supplement contains eight specially commissioned review articles, in which leading experts discuss the application of computational modeling to a range of problems in contemporary neuroscience; topics include dendritic processing, stabilization of neuronal firing rates, short term memory, sensorimotor transformations, object recognition, control of movement, cerebellar function and attention. In addition to the reviews, the supplement contains six History pieces, which highlight some of the most influential theoretical models of the previous half-century, and six Viewpoints, in which prominent theoretical and experimental neuroscientists offer their personal views on the proper role of modeling in neuroscience.