A major shift is happening within neurophysiology: a population doctrine is drawing level with the single-neuron doctrine that has long dominated the field. Population-level ideas have so far had their greatest impact in motor neurophysiology, but they hold incredible promise for resolving open questions in cognition. Here, we codify the population doctrine and survey recent work that leverages this view to probe cognition. Our discussion is organized around five core concepts that provide a foundation for population-level thinking: (1) state spaces, (2) manifolds, (3) coding dimensions, (4) subspaces, and (5) dynamics. The work we review illustrates the progress and promise that population neurophysiology holds for cognitive neuroscience$-$for delivering new insight into attention, working memory, decision-making, executive function, and learning.