In 1998, Jones suggested a classification of thalamocortical projections into core and matrix divisions (Jones, 1998). In this classification, core projections are specific, topographical, innervate middle cortical layers, and serve to transmit specific information to the cortex for further analysis; matrix projections, in contrast, are diffuse, much less topographic, innervate upper layers, especially Layer 1, and serve a more global, modulatory function, such as affecting levels of arousal. This classification has proven especially influential in studies of thalamocortical relationships. Whereas it may be the case that a clear subset of thalamocortical connections fit the core motif, since they are specific, topographic, and innervate middle layers, we argue that there is no clear evidence for any single class that encompasses the remainder of thalamocortical connections as is claimed for matrix. Instead, there is great morphological variation in connections made by thalamocortical projections fitting neither a core nor matrix classification. We thus conclude that the core/matrix classification should be abandoned, because its application is not helpful in providing insights into thalamocortical interactions and can even be misleading. As one example of the latter, recent suggestions indicate that core projections are equivalent to first-order thalamic relays (i.e., those that relay subcortical information to the cortex) and matrix to higher-order relays (i.e., those that relay information from one cortical area to another), but available evidence does not support this relationship. All of this points to a need to replace the core/matrix grouping with a more complete classification of thalamocortical projections.