Anisotropic hydrodynamics: Motivation and methodology

In this proceedings contribution I review recent progress in our understanding of the bulk dynamics of relativistic systems that possess potentially large local rest frame momentum-space anisotropies. In order to deal with these momentum-space anisotropies, a reorganization of relativistic viscous hydrodynamics can be made around an anisotropic background, and the resulting dynamical framework has been dubbed "anisotropic hydrodynamics". I also discuss expectations for the degree of momentum-space anisotropy of the quark-gluon plasma generated in relativistic heavy ion collisions at RHIC and LHC from second-order viscous hydrodynamics, strong-coupling approaches, and weak-coupling approaches. (C) 2014 Elsevier B.V. All rights reserved.