Galaxy groups are more than an intermediate scale between clusters and halos hosting individual galaxies, they are crucial laboratories capable of testing a range of astrophysics from how galaxies form and evolve to large scale structure (LSS) statistics for cosmology. Cosmological hydrodynamic simulations of groups on various scales offer an unparalleled testing ground for astrophysical theories. Widely used cosmological simulations with ~(100 Mpc)^3 volumes contain statistical samples of groups that provide important tests of galaxy evolution influenced by environmental processes. Larger volumes capable of reproducing LSS while following the redistribution of baryons by cooling and feedback are essential tools necessary to constrain cosmological parameters. Higher resolution simulations can currently model satellite interactions, the processing of cool (T~10^4 K) multi-phase gas, and non-thermal physics including turbulence, magnetic fields, and cosmic ray transport. We review simulation results regarding the gas and stellar contents of groups, cooling flows and the relation to the central galaxy, the formation and processing of multi-phase gas, satellite interactions with the intragroup medium, and the impact of groups for cosmological parameter estimation. Cosmological simulations provide evolutionarily consistent predictions of these observationally difficult-to-define objects, and have untapped potential to accurately model their gaseous, stellar, and dark matter distributions.
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