What are the properties of strongly interacting matter and how do they emerge from the fundamental laws of non-abelian gauge theory? For non-abelian plasmas at very high energy density (above the deconfinement transition), this question is studied non-perturbatively via finite temperature lattice theory and - more recently - gauge/gravity duality. Comparing results from these approaches to those of perturbative techniques, a detailed picture arises now of how equilibration processes, transport properties and the propagation of hard processes change with coupling strength, and in which sense non-abelian plasmas must {it not} be viewed as a heat-bath of (quasi-)particles. I review these recent theoretical developments, and I discuss how they enter the phenomenological modeling of relativistic heavy ion collisions at the LHC and at RHIC. The interplay between theory and experiment will be argued to support a conjectured 'standard model' of relativistic heavy ion collisions, and opportunities for further scrutinizing this picture will be discussed.