In this chapter, we review computer models of cognition that have focused on the use of neural networks. These architectures were inspired by research into how computation works in the brain. The approach is called connectionism because it proposes that processing is characterized by patterns of activation across simple processing units connected together into complex networks, with knowledge stored in the strength of the connections between units. We place connectionism in its historical context, describing the “three ages” of artificial neural network research: from the genesis of the first formal theories of computation in the 1930s and 1940s, to the parallel distributed processing (PDP) models of cognition of the 1980s and 1990s, and the advances in “deep” neural networks emerging in the mid-2000s. Transition between the ages has been triggered by new insights into how to create and train more powerful artificial neural networks. We discuss important foundational cognitive models that illustrate some of the key properties of connectionist systems, and indicate how the novel theoretical contributions of these models arose from their key computational properties. We consider how connectionist modeling has influenced wider theories of cognition, and how in the future, connectionist modeling of cognition may progress by integrating further constraints from neuroscience and neuroanatomy.