We sketch a framework for building a unified science of cognition. This unification is achieved by showing how functional analyses of cognitive capacities can be integrated with the multilevel mechanistic explanations of neural systems. The core idea is that functional analyses are sketches of mechanisms, in which some structural aspects of a mechanistic explanation are omitted. Once the missing aspects are filled in, a functional analysis turns into a full-blown mechanistic explanation. By this process, functional analyses are seamlessly integrated with multilevel mechanistic explanations.