Cell crawling is ubiquitous in many biological processes from development to cancer. It is inherently a problem of mechanics, in which forces actively generated by the cell through consumption of chemical energy are transmitted to the environment through transient adhesion to allow for cell translocation. Spreading and crawling cells display rich non-linear dynamics reminiscent of excitable systems. These include periodic phases of growth and retraction of cellular protrusion, travelling waves along the cell edges, and spontaneous cell polarisation and crawling. I will discuss a theoretical model combining the stochasticity of cell-substrate adhesion and linear cell visco-elastic mechanics, in which the force-sensitive unbinding of adhesion bonds leads to a stick-slip dynamics. The model that recapitulate many of the remarkable dynamical features of crawling cells and illustrates the fundamental role of mechanics in regulating cell motility.