By linking the past with the future, our memories define our sense of identity. Because human memory engages the conscious realm, its examination has historically been approached from language and introspection and proceeded largely along separate parallel paths in humans and other animals. Here, we first highlight the achievements and limitations of this mind-based approach and make the case for a new brain-based understanding of declarative memory with a focus on hippocampal physiology. Next, we discuss the interleaved nature and common physiological mechanisms of navigation in real and mental spacetime. We suggest that a distinguishing feature of memory types is whether they subserve actions for single or multiple uses. Finally, in contrast to the persisting view of the mind as a highly plastic blank slate ready for the world to make its imprint, we hypothesize that neuronal networks are endowed with a reservoir of neural trajectories, and the challenge faced by the brain is how to select and match preexisting neuronal trajectories with events in the world.