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Collective motion, which is ubiquitous in nature, has traditionally been explained by “self-propelled particle” models from theoretical physics. Here we show, through field, lab, and virtual reality experimentation, that classical models of collective behavior cannot account for how collective motion emerges in marching desert locusts, whose swarms affect the livelihood of millions. In contrast to assumptions made by these models, locusts do not explicitly align with neighbors. While individuals respond to moving-dot stimuli through the optomotor response, this innate behavior does not mediate social response to neighbors. Instead, locust marching behavior, across scales, can be explained by a minimal cognitive framework, which incorporates individuals’ neural representation of bearings to neighbors and internal consensus dynamics for making directional choices. Our findings challenge long-held beliefs about how order can emerge from disorder in animal collectives.