<p>Animal behavior arises from the coordinated activity of neural populations that span the entire brain. The activity of large neural populations from an increasing number of brain regions, behaviors and species shows low-dimensional structure. We posit that this structure arises as a result of neural manifolds. Neural manifolds are mathematical descriptions of a meaningful biological entity: the possible collective states of a population of neurons given the constraints, both intrinsic (for example, connectivity) and extrinsic (for example, behavior), to the neural circuit. Here, we explore the link between neural manifolds and behavior, and discuss the insights that the neural manifold framework can provide into brain function. To conclude, we explore existing conceptual gaps in this framework and discuss their implications when building an integrative view of brain function. We thus position neural manifolds as a crucial framework with which to describe how the brain generates behavior.</p>