Directed cell motility is a process whereby the motility machinery of the cell (involving the interaction of actin with myosin) is organized spatially so as to cause directed motion. In Dictyostelium, this occurs as the cell responds to cAMP gradients during the aggregation process. In keratocytes, the cell spontaneously polarizes itself (without external cues). This talk will focus on spatially extended modeling of both the signaling system which encodes the directional information and the downstream mechanical response and the comparison of these models to detailed experimental studies of both of these systems.