Cells migrate on surfaces by protruding their front through growth of actin networks, retracting the rear by myosin-driven contraction and adhering to the substrate. Recent experimental and modeling efforts elucidated specific molecular and mechanical processes that allow motile cells to maintain constant distances from front to rear and from side to side while maintaining steady locomotion. Remarkably, these processes are multiple and redundant, and one of the future modeling challenges is a synthesis of these processes (operating on multiple scales) within a computational framework. Necessarily, such framework have to treat the cell as an object with a free boundary leading to a very nontrivial mathematical problem. I will describe initial successes in modeling the simplest motile cell, fish keratocyte, and discuss future challenges in simulating more complex cells.