Computational memory models can explain the behaviour of human memory in diverse experimental paradigms—whether it be recall or recognition, short-term or long-term retention, implicit or explicit learning. Simulation has led to parsimonious theories of memory, but at a cost of a profusion of competing models. As different models focus on different phenomena, there is no best model. However, the models share many characteristics, indicating wide agreement on the mathematics of how memory works in the brain. On the basis of an analysis of computational memory models, we argue that these models can be understood in terms of a single neurally-plausible computational and theoretical framework. We present a proof of concept neural implementation, integration with the ACT-R cognitive architecture, and demonstrate model performance on procedural, declarative, episodic, and semantic learning tasks. This research aims to advance cognitive psychology towards a single integrated, computational model of human memory that can account for human performance on diverse experimental tasks, that can be implemented at a neural level of detail, and can be scaled to modelling arbitrarily long-term learning.