  The core structure of galaxy clusters is fundamentally important. Even though
self-gravitating systems have no stable equilibrium state due to their negative
heat capacity, numerical simulations find density profiles which are universal
in the sense that they are fairly flat within a scale radius and gradually
steepen farther outward, asymptotically approaching a logarithmic slope of
$\approx-3$ near the virial radius. We argue that the reason for the formation
of this profile is not satisfactorily understood. The ratio between the virial
radius and the scale radius, the so-called concentration, is found in
simulations to be closely related to the mass and the redshift and low for
cluster-sized haloes, but observed to be substantially higher at least in a
subset of observed clusters. Haloes formed from cold dark matter should
furthermore be richly substructured. We review theoretical and observational
aspects of cluster cores here, discuss modifications by baryonic physics and
observables that can provide better insight into the internal structure of
clusters.
