Cell migration is essential for development and tissue repair, and is crucial for tumorigenesis. It is unclear whether a general rule can account for the diversity of cell migration patterns observed in vivo and in vitro. By analysing trajectories of cells migrating in live tissues and under various in vitro conditions, Maiuri et al. revealed a universal coupling between cell migration speed and cell persistence (the capacity to maintain the direction of motion). The authors developed a physical model to explain how faster cells move straighter. In this model, coupling between cell speed and persistence relies on cellular actin retrograde flows that transport polarity cues from the front to the rear of migrating cells. The model, which was validated experimentally by optogenetic modulation of actin retrograde flows, can predict cell trajectories and could thus be used for the study of processes such as metastasis.