It has been widely observed that when artificial neural networks are trained by supervised learning to do computations that also occur in the nervous system, the behavior of the model neurons often closely resembles that of the real neurons involved in the task. It is not immediately clear why this should be the case or what use can be made of models generated by supervised learning. Here, recent developments are reviewed and analysed in an attempt to clarify these issues. This analysis is facilitated by treating supervised learning models of the brain as a special case of system identification, a general and well-studied modeling paradigm. The neural systems identification paradigm provides a systematic way to generate realistic models starting with a high-level description of a hypothesized computation and some architectural and physiological constraints about the area being modeled. There is no inherent limitation to the realism that can be incorporated into identification models. This approach eliminates the need to find neural implementation algorithms by ad hoc means and provides neuroscientists with a convenient way to build models that account for observed data.