The shape of eukaryotic cells is determined by structural proteins (such as actin) collectively known as the cytoskeleton. For example, localized assembly of filamentous actin (F-actin) leads to protrusion of parts of the cell outwards, whereas activation of myosin powers contraction. Here I will talk about our recent mathematical modeling of cellular signaling. We study the signaling that regulates the assembly of F-actin, and the resultant effects on dynamics of cell shape, cell motility, and single-cell wound healing. I will describe how we used ordinary and partial differential equations to investigate the activities of regulatory proteins (small GTPases) that regulate the cytoskeleton, and how our methods helped to gain insight into mechanisms underlying experimentally observed cellular behaviour.