In this review, we have examined recent studies that have successfully identified neural circuits necessary for nonspecific and specific conditioned responses. This success is due in large part to the advantages of the classical conditioning paradigm for controlling stimuli and responses. Clearly, this research does not attempt to account for all forms of memory. The power of this approach is demonstrated by the distinction between essential and nonessential memory traces or engrams. Essential memory traces represent the circuitry responsible for forming the association in classical conditioning. Nonessential memory traces do not represent the essential association, but they are important for facilitating, adapting, and modifying the final performance of the learned behavior. The search for the engram for any learned behavior has been viewed with skepticism by some investigators who quote Karl Lashley: "This series of experiments has yielded a good bit of information about what and where the memory is not. It has discovered nothing directly of the real nature of the engram" (1950, pp. 477-78). However, these authors neglect to quote Lashley fully, for even he was less pessimistic about that search than in normally recognized. He continued, "I sometimes feel, in reviewing the evidence on the localization of the memory trace, that the necessary conclusion is that learning just is not possible. It is difficult to conceive of a mechanism which can satisfy the conditions set for it. Nevertheless, in spite of such evidence against it, learning does sometimes occur" (1950, pp. 477-78, emphasis added). Learning does indeed occur, and its neurobiological substrates can be localized.