The principal interactions leading to the emergence of order in swarms of marching locust nymphs was studied both experimentally, using small groups of marching locusts in the lab, and using computer simulations. We utilized a custom tracking algorithm to reveal fundamental animal-animal interactions leading to collective motion. Uncovering this behavior introduced a new agent-based modeling approach in which pause-and-go motion is pivotal. The behavioral and modeling findings are largely based on motion-related visual sensory inputs obtained by the individual locust. Results suggest a generic principle, in which intermittent animal motion can be considered as a sequence of individual decisions as animals repeatedly reassess their situation and decide whether or not to swarm. This interpretation implies, among other things, some generic characteristics regarding the build-up and emergence of collective order in swarms: in particular, that order and disorder are generic meta-stable states of the system, suggesting that the emergence of order is kinetic and does not necessarily require external environmental changes. This work calls for further experimental as well as theoretical investigation of the neural mechanisms underlying locust coordinative behavior.