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, corrects errors and integrates noisy cues. We consider the mechanisms by which simple and forgetful units can organize to collectively generate dynamics on the long timescales 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 highlight recent theoretical advances in understanding how the fundamental trade-offs 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.
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