The most massive baryonic component of galaxy clusters is the ‘intracluster medium’ (ICM), a diffuse, hot, weakly magnetized plasma that is most easily observed in the X-ray band. Despite being observed for decades, the macroscopic transport properties of the ICM are still not well constrained. A path to determine macroscopic ICM properties opened up with the discovery of ‘cold fronts’. These were observed as sharp discontinuities in surface brightness and temperature in the ICM, with the property that the denser side of the discontinuity is the colder one. The high spatial resolution of the Chandra X-ray Observatory revealed two puzzles about cold fronts. First, they should be subject to Kelvin–Helmholtz instabilities, yet in many cases they appear relatively smooth and undisturbed. Second, the width of the interface between the two gas phases is typically narrower than the mean free path of the particles in the plasma, indicating negligible thermal conduction. It was thus realized that these special characteristics of cold fronts may be used to probe the properties of the cluster plasma. In this review, we will discuss the recent simulations of cold fronts in galaxy clusters, focusing on those which have attempted to use these features to constrain ICM physics. In particular, we will examine the effects of magnetic fields, viscosity, and thermal conductivity on the stability properties and long-term evolution of cold fronts. We conclude with a discussion on what important questions remain unanswered, and the future role of simulations and the next generation of X-ray observatories.