Over the years, the General Theory has been as controversial as it has been influential. However, many of the controversies have been fanned by misunderstandings of the General Theory. In addition, resolution to the controversies were sometimes delayed because the models used to account for specific phenomena were not yet developed. This chapter addresses these controversies by showing how specific empirical phenomena once thought by some to challenge the General Theory are actually predicted a priori by retrieving effectively from memory (REM) models originally designed to account for forgetting.

An often overlooked, but important, influence on human memory is prior testing. In this chapter, search of associative memory (SAM) and retrieving effectively from memory (REM) models of effects of memory testing are described, as applied to recall and recognition procedures. In addition, problems associated with not taking into account the consequences of testing are illustrated through a discussion of ongoing research on the von Restorff effect.

The formal details of the modeling frameworks that have been most useful in accounting for specific empirical phenomena are presented. At the highest, most abstract level are mathematical models used to describe how the contents of the short-term store are managed. At the middle level, the search of associative memory models (SAM) describe how information is transferred from the short-term store to the long-term store, and how memories in the long-term store are retrieved to the short-term store. At the lowest, most complex level, the retrieving effectively from memory (REM) models are described, which implement multidimensional memory representations and rational decision processes.

The foundations of the General Theory are described at a conceptual level of understanding. The basic terminology of memory research is presented. The main focus is on the proposed memory structures and the control processes that guide the flow of information though them. The assumed memory structures are sensory registers, the short-term store, and the long-term store. Control processes are models of the flow information through these structures to support the performance of tasks that lead to the achievement of a subjective goal. Empirical support for the fundamental assumptions of the General Theory are provided.

Forgetting is a phenomenon that is familiar to everyone and among the most extensively investigated in psychological science. It is, therefore, quite surprising that forgetting is widely misunderstood by the layperson and even by researchers. Evidence for the permanence of long-term memories is presented, and the distinction between the accessibility and availability of memories is discussed. Search of associative memory (SAM) and retrieving effectively from memory (REM) models of forgetting are described and extended as a proposal for everyday forgetting.

In the 1980s there was surge of interest in modeling human memory. One of the most successful lines of research investigated recognition memory, and several important models were developed. Testing of the models was conducted, leading to a consensus that there were problems with all extant models. This led to the development of more complex models that assumed that differentiation was an important process in human memory. The findings that challenged then extant models are presented, and the retrieving effectively from memory (REM) framework describing differentiation is discussed in detail.

With development of the retrieving effectively from memory (REM) modeling framework, research on the interaction of experience and knowledge has taken off. While in its infancy, several models of lexical access have been developed. These models have more recently been extended to describe how experience leads to knowledge. Both the strengths and limitations of the current models are described.

Investigations of the contribution of controlled versus automatic information processing are presented using two superficially different procedures as examples: visual search and episodic recognition memory. Whereas most frameworks consider the possibility that tasks may be performed either in a controlled fashion or automatically, the General Theory assumes that both types of information processing may contribute to their performance. Thus, the empirical question is the extent to which each type of information processing contributes to task performance and under what conditions.

Sequential effects are among the most robust phenomena observed in psychological experiments; judgments that may be made independently are influenced by prior judgments when made in a sequence, even when doing so is suboptimal. Over the years, models of sequential effects that are observed in categorization, recognition, absolute identification, and short-term priming experiments were developed by different researchers at different times, each apparently unaware of the others. Nevertheless, all models of sequential effects developed within the framework of the General Theory converged on the same assumption: information used to make one judgment carries over to influence the judgment made on a subsequent trial. These models and relevant data are presented.