  A classification of gravitating Yang--Mills systems in all dimensions is
presented. These systems are set up so that they support finite energy
solutions. Both regular and black hole solutions are considered, the former
being the limit of the latter for vanishing event horizon radius. Special
attention is paid to systems necessarily involving higher order Yang--Mills
curvature terms, along with the option of incorporating higher order terms in
the Riemann curvature. The scope here is restricted to Einstein systems, with
or without cosmological constant, and the Yang--Mills(--Higgs) systems.
