Cells crawl and reorganize in the body to perform their functions, ranging from white blood cells finding bacteria to skin cells closing over a wound. Modeling cell motility provides interesting challenges, both because cells must deal with a noisy, fluctuating environment - but also because cells can modify their own environment. I will discuss two examples of how my group has explored these topics. First, I will discuss the physical and statistical limits that control cells' ability to respond to electric fields, which help guide cells to help heal wounds. This analysis sets a limit bounding how accurately cells can sense the field, and predicts a universal form of the cell's directionality as a function of field strength. Secondly, I will talk about how cells interact with their own "footprints" - chemicals that the cell deposits to mark where it has traveled.  This footprint deposition allows cells to switch between different types of motility - oscillating back and forth or persistent migration of different degrees of confinement. We show that we can recapitulate many experimental results by assuming that the footprint regulates the cells' Rho GTPase-based polarity.