Reductionism is one of the most divisive concepts in the popular and philosophical lexicon. Over the past century it has been championed, declared dead, resurrected, and reformed many times over. This chapter sketches the goals and methods of one prominent form of reductionism within the mind-brain sciences and considers the prospects for non-reductionist alternatives. Reductive explanation is an interfield project. A field centers on a set of problems, relevant facts, and phenomena that bear on their solutions, explanatory goals and norms, and distinctive experimental techniques, materials, and methods. Cognitive modeling is one of the main tools used in psychology to describe and understand the mental and behavioral capacities of humans and other organisms. Mechanisms are organized sets of entities plus their associated activities and processes. The success of mechanistic reduction turns on the existence of a smooth mapping from cognitive models onto neural mechanisms.