Some theorists who emphasize the complexity of biological and cognitive systems and who advocate the employment of the tools of dynamical systems theory in explaining them construe complexity and reduction as exclusive alternatives. This paper argues that reduction, an approach to explanation that decomposes complex activities and localizes the components within the complex system, is not only compatible with an emphasis on complexity, but provides the foundation for dynamical analysis. Explanation via decomposition and localization is nonetheless extremely challenging, and an (...) analysis of recent cognitive neuroscience research on memory is used to illustrate what is involved. Memory researchers split between advocating memory systems and advocating memory processes, and I argue that it is the latter approach that provides the critical sort of decomposition and localization for explaining memory. The challenges of linking distinguishable functions with brain processes is illustrated by two examples: competing hypotheses about the contribution of the hippocampus and competing attempts to link areas in frontal cortex with memory processing. (shrink)