All is flux, nothing stays still. Heraclitus of Ephesus’ characterization of the universe holds true for cells within animals and for proteins within cells. In this review, we examine the dynamics of actin and non-muscle myosin II within cells, and how their dynamics power the movement of cells within tissues. The 3D environment that migrating cells encounter along their path also changes over time, and cells can adopt various mechanisms of motility, depending on the topography, mechanics and chemical composition of their surroundings. We describe the differential spatio-temporal regulation of actin and myosin II-mediated contractility in mesenchymal, lobopodial, amoeboid, and swimming modes of cell migration. After briefly reviewing the biochemistry of myosin II, we discuss the role actomyosin contractility plays in the switch between modes of 3D migration that cells use to adapt to changing environments.