The paper is an examination of the ways and extent to which neuroscience places constraints on cognitive science. In Part I, I clarify the issue, as well as the notion of levels in cognitive inquiry. I then present and address, in Part II, two arguments designed to show that facts from neuroscience are at a level too low to constrain cognitive theory in any important sense. I argue, to the contrary, that there are several respects in which facts from neurophysiology will constrain cognitive theory. Part III then turns to an examination of Connectionism and Classical Cognitivism to determine which, if either, is in a better position to accomodate neural constraints in the ways suggested in Part II.