Many neuroscientists, cognitive scientists and philosophers take it that nervous systems, and even their single cells, perform computations and that these computational operations play a role in producing and explaining cognition. Scientists and philosophers also tend to account for neuro-cognitive phenomena within one or another framework of levels. This chapter focuses on on-going debates concerning the place of computational explanations within a leveled approach to the study of neuro-cognitive phenomena. It begins with a picture that deals with scientific practice in general, but greatly influenced frameworks for explanation in cognitive science. An influential position in philosophy of cognitive science, advocated mostly at the end of the twentieth century, is that cognitive capacities are explained by appeal to cognitive functions and their interaction. The mechanistic approach to explanation in the cognitive and neural sciences has been widely advocated in recent years.