  We present the Rhapsody-G suite of cosmological hydrodynamic AMR zoom
simulations of ten massive galaxy clusters at the $M_{\rm vir}\sim10^{15}\,{\rm
M}_\odot$ scale. These simulations include cooling and sub-resolution models
for star formation and stellar and supermassive black hole feedback. The sample
is selected to capture the whole gamut of assembly histories that produce
clusters of similar final mass. We present an overview of the successes and
shortcomings of such simulations in reproducing both the stellar properties of
galaxies as well as properties of the hot plasma in clusters. In our
simulations, a long-lived cool-core/non-cool core dichotomy arises naturally,
and the emergence of non-cool cores is related to low angular momentum major
mergers. Nevertheless, the cool-core clusters exhibit a low central entropy
compared to observations, which cannot be alleviated by thermal AGN feedback.
For cluster scaling relations we find that the simulations match well the
$M_{500}-Y_{500}$ scaling of Planck SZ clusters but deviate somewhat from the
observed X-ray luminosity and temperature scaling relations in the sense of
being slightly too bright and too cool at fixed mass, respectively. Stars are
produced at an efficiency consistent with abundance matching constraints and
central galaxies have star formation rates consistent with recent observations.
While our simulations thus match various key properties remarkably well, we
conclude that the shortcomings strongly suggest an important role for
non-thermal processes (through feedback or otherwise) or thermal conduction in
shaping the intra-cluster medium.
