The accumulation and storage of information in memory is a fundamental computation underlying animal behavior. In many brain regions and task paradigms, ranging from motor control to navigation to decision-making, such accumulation is accomplished through neural integrator circuits that enable external inputs to move a system’s population-wide patterns of neural activity along a continuous attractor. In the first portion of the talk, I will discuss our efforts to dissect the circuit mechanisms underlying a neural integrator from a rich array of anatomical, physiological, and perturbation experiments. In the second portion of the talk, I will show how the accumulation and storage of information in long-term memory may also be described by attractor dynamics, but now within the space of synaptic weights rather than neural activity. Altogether, this work suggests a conceptual unification of seemingly distinct short- and long-term memory processes.