  Relativistic hydrodynamics has been extensively applied to high energy
heavy-ion collisions. We review hydrodynamic calculations for Au+Au collisions
at RHIC energies and provide a comprehensive comparison between the model and
experimental data. The model provides a very good description of all measured
momentum distributions in central and semiperipheral Au+Au collisions,
including the momentum anisotropies (elliptic flow) and systematic dependencies
on the hadron rest masses up to transverse momenta of about 1.5--2 GeV/c. This
provides impressive evidence that the bulk of the fireball matter shows
efficient thermalization and behaves hydrodynamically. At higher p_t the
hydrodynamic model begins to gradually break down, following an interesting
pattern which we discuss. The elliptic flow anisotropy is shown to develop
early in the collision and to provide important information about the early
expansion stage, pointing to the formation of a highly equilibrated quark-gluon
plasma at energy densities well above the deconfinement threshold. Two-particle
momentum correlations provide information about the spatial structure of the
fireball (size, deformation, flow) at the end of the collision. Hydrodynamic
calculations of the two-particle correlation functions do not describe the data
very well. Possible origins of the discrepancies are discussed but not fully
resolved, and further measurements to help clarify this situation are
suggested.
