Computational cognitive neuroscience lies at the intersection of computational neuroscience, which aims to describe structures and processes in the brain through computational modeling and mathematical analysis, and cognitive neuroscience, which aims to explain behavior and cognition through the identification and description of neural mechanisms. This chapter provides a methodological overview of computational cognitive neuroscience, centering on a distinction between two widely used research strategies. On the one hand, top-down strategies are used to infer, from formal characterizations of behavior and cognition, the function and structure of neural mechanisms. On the other hand, bottom-up strategies are used to identify and describe neural mechanisms and their formal properties, and to reconstruct their contributions to specific kinds of behavior and cognition. Many research efforts in computational cognitive neuroscience can be viewed as instances of either the top-down or the bottom-up research strategy.