We seek to understand the brain’s algorithms and how they emerge from the interplay between neural activity and network dynamics. By combining rodent electrophysiology, behavior, and computational modeling, we investigate fundamental algorithms such as path integration and pattern separation, which underlie spatial navigation and memory formation. Our discoveries—such as characterizing cell types in the entorhinal cortex and uncovering the computational role of adult-born neurons in the hippocampus—highlight how neural circuits adapt and self-organize for efficient information processing. We also examine how these mechanisms break down in neurodegeneration, exemplified by the first-ever studies of hippocampal activity in Octodon degus, a South American rodent that naturally recapitulates sporadic Alzheimer’s disease. By focusing on emergent properties in circuits of the hippocampal formation, we aim to uncover principles of neural computation and their relevance to health and disease.