Although James Anderson (e.g., 1973) and Steve Grossberg (e.g., 1970) had proposed distributed composite memory systems in the 1970's, the first well-worked-out model of this sort that was applied to many of the phenomena of memory was proposed by Murdock (e.g., the TODAM model, 1982) and his student, Janet Metcalfe (e.g., Eich, 1982). With the growth of interest in neural net and connectionist models, the fundamental assumption that memory is represented through composition and distribution is of paramount importance. We propose to address this assumption in this chapter, albeit briefly. As we shall see, there is a closely related question upon which the data bear even more strongly, concerning whether the limitations of memory are inherent in the structure of memory that is formed at storage or inherent in the processes of retrieval from memory. These are different issues in theory but highly correlated in practice.