  Dense star clusters are spectacular self-gravitating stellar systems in our
Galaxy and across the Universe - in many respects. They populate disks and
spheroids of galaxies as well as almost every galactic center. In massive
elliptical galaxies nuclear clusters harbor supermassive black holes, which
might influence the evolution of their host galaxies as a whole. The evolution
of dense star clusters is not only governed by the aging of their stellar
populations and simple Newtonian dynamics. For increasing particle number,
unique gravitational effects of collisional many-body systems begin to dominate
the early cluster evolution. As a result, stellar densities become so high that
stars can interact and collide, stellar evolution and binary stars change the
dynamical evolution, black holes can accumulate in their centers and merge with
relativistic effects becoming important. Recent high-resolution imaging has
revealed even more complex structural properties with respect to stellar
populations, binary fractions and compact objects as well as - the still
controversial - existence of intermediate mass black holes in clusters of
intermediate mass. Dense star clusters therefore are the ideal laboratory for
the concomitant study of stellar evolution and Newtonian as well as
relativistic dynamics. Not only the formation and disruption of dense star
clusters has to be considered but also their galactic environments in terms of
initial conditions as well as their impact on galactic evolution. This review
deals with the specific computational challenges for modelling dense,
gravothermal star clusters.
