Many X-ray observations of relaxed galaxy clusters reveal the presence of sharp, spiral-shaped discontinuities in the surface brightness of the X-ray emitting gas. Spectral analysis of these features shows that the colder gas is on the brighter side, hence they have been dubbed "cold fronts." These features arise naturally in simulations from the cool-core gas "sloshing" in the gravitational potential. Their sharpness and stability has important implications for the microphysics of the ICM. The sloshing motions may have other effects, such as contributing to the heating of the cluster core and the acceleration of relativistic particles. I will present simulations of gas sloshing in clusters, explain their formation and evolution, and discuss the implications for the physics of the ICM.