  We review several facets of the hydrodynamic description of the relativistic
heavy ion collisions, starting from the historical motivation to the present
understandings of the observed collective aspects of experimental data,
especially those of the most recent RHIC and LHC results. In this report, we
particularly focus on the conceptual questions and the physical foundations of
the validity of the hydrodynamic approach itself. We also discuss recent
efforts to clarify some of the points in this direction, such as the various
forms of derivations of relativistic hydrodynamics together with the
limitations intrinsic to the traditional approaches, variational approaches,
known analytic solutions for special cases, and several new theoretical
developments. Throughout this review, we stress the role of course-graining
procedure in the hydrodynamic description and discuss its relation to the
physical observables through the analysis of a hydrodynamic mapping of a
microscopic transport model. Several questions to be answered to clarify the
physics of collective phenomena in the relativistic heavy ion collisions are
pointed out.
