Karl Lashley began the search for the engram nearly seventy years ago. In the time since, much has been learned but divisions remain. In the contemporary neurobiology of learning and memory, two profoundly different conceptions contend: the associative/connectionist (A/C) conception and the computational/representational (C/R) conception. Both theories ground themselves in the belief that the mind is emergent from the properties and processes of a material brain. Where these theories differ is in their description of what the neurobiological substrate of memory is and where it resides in the brain. The A/C theory of memory emphasizes the need to distinguish memory cognition from the memory engram and postulates that memory cognition is an emergent property of patterned neural activity routed through engram circuits. In this model, learning re-organizes synapse association strengths to guide future neural activity. Importantly, the version of the A/C theory advocated for here contends that synaptic change is not symbolic and, despite normally being necessary, is not sufficient for memory cognition. Instead, synaptic change provides the capacity and a blueprint for reinstating symbolic patterns of neural activity. Unlike the A/C theory, which posits that memory emerges at the circuit level, the C/R conception suggests that memory manifests at the level of intracellular molecular structures. In C/R theory, these intracellular structures are information-conveying and have properties compatible with the view that brain computation utilizes a read/write memory, functionally similar to that in a computer. New research has energized both sides and highlighted the need for new discussion. Both theories, the key questions each theory has yet to resolve and several potential paths forward are presented here.