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 towards out-of-equilibrium systems is addressed, emphasizing the so-called attractor solution. On the other hand, 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 the three-dimensionally expanding quark-gluon plasma, the fluid description of small colliding systems, and some other interdisciplinary connections are discussed.