  Fluid dynamic approach is a workhorse for modelling collective dynamics in
relativistic heavy-ion collisions. The approach has been successful in
describing various features of the momentum distributions of hadrons produced
in the heavy-ion collisions, such as $p_T$ spectra, flow coefficients $v_n$
etc. As such, the description of the phenomenon of polarization of $\Lambda$
hyperons in heavy-ion collisions has to be incorporated into the hydrodynamic
approach. We start this chapter by introducing different definitions of
vorticity in relativistic fluid dynamics. Then we present a derivation of the
polarization of spin 1/2 fermions in the relativistic fluid. The latter is
directly applied to compute the spin polarization of the $\Lambda$ hyperons,
which are produced from the hot and dense medium, described with fluid
dynamics. It is followed by a review of the existing calculations of global or
local polarization of $\Lambda$ hyperons in different hydrodynamic models of
relativistic heavy-ion collisions. We particularly focus on the explanations of
the collision energy dependence of the global $\Lambda$ polarization from the
different hydrodynamic models, the polarization component in the beam direction
as well as on the origins of the global and local $\Lambda$ polarization.
