Cell migration is an essential process, involved in immune defense, cancer spread, wound healing, and embryo development. This work presents modeling efforts to understand various mechanisms of cell migration. We first discuss the modeling of bleb-driven cell migration, where the cell membrane detaches from the cytoskeleton and generates a protrusion that is completely devoid of structural proteins. Cell migration in this case is driven essentially by pressure and motor contractility exerted by myosin. I will introduce a stochastic model of bleb-driven migration offering support for theories on blebbing cell polarization and the potential involvement of water channels. We then turn to the involvement of ion channels and ionic electrodiffusion in cell processes, first in cell volume control, and then in cell migration, presenting a model that combines electrodiffusion-driven migration with a mechanical model of actin polymerization.