The development of the sequential approach to instrumental learning from about 1958 to the present is described. The sequential model began as an attempt to explain a particular class of neglected partial reward phenomena, those in which performance in acquisition and extinction is influenced by the particular sequence in which rewarded and nonrewarded trials occur in acquisition, and it was subsequently applied to a variety of other phenomena. Over time, the sequential model grew, sometimes through the replacement of older assumptions by novel ones, as when retrieved memories replaced stimulus traces, and sometimes simply through the addition of novel assumptions, such as that animals are capable of remembering retrospectively one, two, three or more prior nonrewarded outcomes—the N-length assumption. The most recent assumption added to the sequential model is that on a given trial the animal may utilize its memory of prior reward outcomes to anticipate both the current reward outcome and one or more subsequent reward outcomes. One way to view the sequential model is to say that it is a specific theory in various degrees of competition with other specific theories. Several examples of this are provided. Another way to view the sequential model, a more important way in my opinion, is to see it as a representative of a general theoretical approach, intertrial theory, which differs in fundamental respects from another much more generally utilized theoretical approach, intra-trial theory. I suggest that there is a substantial body of data that can be explained by inter-trial mechanisms but not by intratrial mechanisms. The future may well reveal that the inter-trial mechanisms have greater explanatory potential than the currently more popular intratrial mechanisms.