Contemporary brain research seeks to understand how cognition is reducible to neural activity. Crucially, much of this effort is guided by a scientific paradigm that views neural activity as essentially driven by external stimuli. In contrast, recent perspectives argue that this paradigm is by itself inadequate, and that understanding patterns of activity intrinsic to the brain is needed to explain cognition. Yet despite this critique, the stimulus-driven paradigm still dominates - possibly because a convincing alternative has not been clear. Here we review a series of experimental findings in the hippocampus suggesting such an alternative. These findings indicate that hippocampal neural activity occurs in one of three brain states that have radically different anatomical, physiological, representational, and behavioral correlates, together implying different roles in cognition. This three-state framework also indicates that hippocampal neural representations follow a surprising pattern of organization at the timescale of ∼1 s or longer. Lastly, beyond the hippocampus, recent breakthroughs indicate three parallel states in cortex, suggesting shared principles and brain-wide organization of intrinsic neural activity. This article is protected by copyright. All rights reserved.