The development ofthe sequential approach to instrumentallearning from about 1958 to the present is described. The sequential model began as an attempt to explain a particular dass 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-Iength 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 generaIly utilized theoretical approach, intratrial theory. I suggest that there is a substantial body of data that can be explained by intertrial mechanisms but not by intratrial mechanisms. The future may weIl reveal that the intertrial mechanisms have greater explanatory potential than the currently more popular intratrial mechanisms.The cognitive abilities of rats are far greater and more varied than was dreamed of even remotely until recently. Even now they are familiar to only a relative few. As Wright (1992) has recently indicated, an animal may perform poorly not because of its cognitive limitations, but because the experimenter has employed a task ill suited to the particular species. Varied reward situations, emphasized in this paper, have demonstrated themselves to be ideally suited to revealing a variety of complex abilities in rats. To be sure, varied reward situations were employed initiaIly to test the simplest of hypotheses. But varied reward situations, as we shall see, are very flexible, and when appropriately modified they can be ernployed in the service of many ends. Within the context ofthe author's sequential hypothesis, varied reward tasks have been repeatedly modified to reveal increasingly complex processes in the rat, an activity that is ongoing.In the present paper, varied reward refers to situations with the following characteristics. Animals receive two or more different reward outcomes, such as food reward Correspondence concerning this article should besent to E. J. Capaldi, Department of Psychological Sciences, Purdue University, 1364 Psychology Building, West ...