  In this review, we describe the singular success of attractor neural network
models in describing how the brain maintains persistent activity states for
working memory, error-corrects, and integrates noisy cues. We consider the
mechanisms by which simple and forgetful units can organize to collectively
generate dynamics on the long time-scales required for such computations. We
discuss the myriad potential uses of attractor dynamics for computation in the
brain, and showcase notable examples of brain systems in which inherently
low-dimensional continuous attractor dynamics have been concretely and
rigorously identified. Thus, it is now possible to conclusively state that the
brain constructs and uses such systems for computation. Finally, we look ahead
by highlighting recent theoretical advances in understanding how the
fundamental tradeoffs between robustness and capacity and between structure and
flexibility can be overcome by reusing and recombining the same set of modular
attractors for multiple functions, so they together produce representations
that are structurally constrained and robust but exhibit high capacity and are
flexible.
