Studying clusters of galaxies with hydrodynamical simulations

I review recent results of cosmological hydrodynamic simulations for clusters of galaxies. Such simulations have developed into an increasingly powerful tool to make theoretical predictions for clusters, and to confront them with observations. I focus, in particular, on the continuing challenge to reproduce the observed cluster X-ray scaling relations in CDM simulations. Self-consistent simulations that include radiative cooling, star formation and supernova feedback generally overpredict the X-ray luminosity on group scales and exhibit overly strong cooling flows. Solving these problems may require the consideration of more physics in cluster simulations, for example thermal conduction or heating by a central AGN.