Cell motility is coordinated by an intricate network of interacting proteins and lipids, that transduce signals into cytoskeletal reorganization, cell shape changes, and locomotion. Here I will survey some mathematical modeling that addresses both normal and aberrant cell motility. I will describe efforts in my group to construct and analyse mathematical models for proteins (such as Rho family GTPases) and lipids (such as phosphoinositides), their feedbacks and their effects on protrusion and contraction of the cell front and rear, as well as cell shape. The role of the cytoskeleton and its actin-associated proteins (e.g. cofilin) will be mentioned. I will describe how several projects on cell polarity and GTPase spatial patterns have contributed to some insights into cell motility.