This chapter was born of an ill-defined but definite feeling that we, as cognitive psychologists, do not really understand our concepts of representation. We propose them, talk about them, argue about them, and try to obtain evidence in support of them, but we do not understand them in any fundamental sense. Anyone who has attempted to read the literature related to cognitive representation quickly becomes confused – and with good reason. The field is obtuse, poorly defined, and embarrassingly disorganized. Among the most popular terms, one finds the following: visual codes, verbal codes, spatial codes, physical codes, name codes, image codes, analog representations, digital representations, propositional representations, first-order isomorphisms, second-order isomorphisms, multidimensional spaces, templates, features, structural descriptions, relational networks, multicomponent vectors, and even holograms. This abundance of language for talking about representation would be a good thing if all the distinctions were clear and if they fit together in a systematic way. The fact is that they are not clear and do not fit together. Different people use the same term in different ways and different terms in the same way. These are not characteristics of a scientific field with a deep understanding of its problem, much less its solution. This chapter is an extended inquiry into the nature of the problem of cognitive representation. The rationale is that a solution is more likely to be achieved if the problem is understood properly.