Cell motility is based on the dynamics of active polymer gels and other macromolecules. The physical state of these dynamic components, and cellular matter in general, is controlled by complex protein and genetic networks. We propose to classify participating molecules into three categories. First, there are the basic structural proteins. Second, the physical state of these structural proteins is set by regulating proteins, which constitute the control parameters of the system. Together, structural and regulating proteins build cellular modules exhibiting distinct dynamic phases and phase transitions. Third, these modules are interlinked by a signaling network determining the functional state of the cell. However, the topology of the ensuing dynamic phase diagram is independent of cellular signaling. In contrast, phase trajectories are set by the signaling network. I discuss examples of such dynamic phases and phase transitions found in cell spreading of mouse embryonic fibroblasts and wing disk cells of drosophila melanogaster, as well as the slime mold physarum polycephalum. Remarkably, there is universal behavior in these evolutionary distant species.