The curvature of a surface determines the migration behavior of biological cells. They preferentially move along valleys or grooves while avoiding ridges. These findings, published in the journal Proceedings of the National Academy of Sciences with contribution from the Max Planck Institute for Dynamics and Self-Organization (MPI-DS) and the Weizmann Institute of Science, give rise to a model predicting cellular behavior. Such universal principles now allow a better understanding of the migration of immune and cancer cells, paving the way for new treatment options.