  Heavy-ion collisions at BNL's Relativistic Heavy Ion Collider and CERN's
Large Hadron Collider provide strong evidence for the formation of a
quark-gluon plasma, with temperatures extracted from relativistic viscous
hydrodynamic simulations shown to be well above the transition temperature from
hadron matter. How the strongly correlated quark-gluon matter forms in a
heavy-ion collision, its properties off-equilibrium, and the thermalization
process in the plasma, are outstanding problems in QCD. We review here the
theoretical progress in this field in weak coupling QCD effective field
theories and in strong coupling holographic approaches based on gauge-gravity
duality. We outline the interdisciplinary connections of different stages of
the thermalization process to non-equilibrium dynamics in other systems across
energy scales ranging from inflationary cosmology, to strong field QED, to
ultracold atomic gases, with emphasis on the universal dynamics of non-thermal
and of hydrodynamic attractors. We survey measurements in heavy-ion collisions
that are sensitive to the early non-equilibrium stages of the collision and
discuss the potential for future measurements. We summarize the current
state-of-the art in thermalization studies and identify promising avenues for
further progress.
