The motions of cells and organelles are highly coordinated. They are driven by motor proteins moving along cytoskeletal filaments, and by the dynamic growth and shrinkage of the filaments themselves. The initiation of cellular motility is triggered by biochemical signaling pathways, but the coordination of motility at different locations or times is not well understood. In this review I discuss a new hypothesis that motility is coordinated through mechanical signals passing between and regulating the activity of motors and filaments. The signals are carried by forces and sensed through the acceleration of protein-protein dissociation rates. Mechanical signaling can lead to spontaneous symmetry breaking, switching, and oscillations, and it can account for a wide range of cell motions such as the flagellar beat, mitotic spindle movements, and bidirectional organelle transport. Because forces can propagate quickly, mechanical signaling is ideal for coordinating motion over large distances.