Over the past two decades connectionist computational models of cognitive processes have come to predominate over traditional symbolic computational models. Whereas, however, it was relatively clear what aspects the parts of the symbolic models mapped on to in the cognitive domain (e.g., concepts, beliefs, desires), it has never been completely clear what the components of connectionist networks (e.g., units, connections) map on to in either the cognitive domain or some other "nearby" domain. Connectionist frequently speak of the "neural inspiration" and "biological plausibility" of the networks, they rarely concede that they are literally engaged in a process of directly modeling the neural organization that is thought to underlie cognition.In this dissertation I attempt to discover exactly what, if anything, connectionist models of cognition model. After briefly surveying the early history of connectionism in chapter l, I go on, in chapter 2, to closely examine the words of connectionists themselves on the issue of what the networks correspond to in the cognitive, neurological, (or other?) domain. Finding no clear answer there, in Chapter 3 I turn to the philosophical literature having to do with scientific explanation and scientific models to see if connectionist practices can be understood in those terms. Although I find some possible parallels in the work of semantic and post-semantic philosophers of science, a coherent account of connectionism does not emerge. Finally, in Chapter 4, I explore directly the claim that connectionist networks are idealized models of the neural structure that underpins cognition. I run several original connectionist simulations, attempting to "add back" neurological details that performance, however, it makes it considerable worse and the adding of extra computational resources do not seem to be able to resolve the new problems. Chapter 5 summarizes the complete argument of the dissertation and identifies the crucial dilemma that I believe to be facing connectionist cognitive science at this point in time.