Recent development of hydrodynamic modeling in heavy-ion collisions

We present a concise review of the recent development of relativistic hydrodynamics and its applications to heavy-ion collisions. Theoretical progress on the extended formulation of hydrodynamics toward out-of-equilibrium systems is addressed, with emphasis on the so-called attractor solution. Moreover, recent phenomenological improvements in the hydrodynamic modeling of heavy-ion collisions with respect to the ongoing beam energy scan program, the quantitative characterization of transport coefficients in three-dimensionally expanding quark-gluon plasma, the fluid description of small colliding systems, and certain other interdisciplinary connections are discussed. (authors)