Acyclic models is a method heavily used to analyze and compare various homology and cohomology theories appearing in topology and algebra. This book attempts to put together in a concise form this important technique and to include all the necessary background. It presents a brief introduction to category theory and homological algebra. It then gives the background of the theory of differential modules and chain complexes over an abelian category to state the main acyclic models theorem, generalizing and systemizing the earlier material. This is then applied to various cohomology theories in algebra and topology.