In recent years, due to the discoveries of hyperon spin polarization and vector meson spin alignment in relativistic heavy-ion collision experiments, the spin transports in quark-gluon matter has received intensive studies. The relativistic spin hydrodynamics is one of the important theoretical frameworks to describe the spin transports, which encodes the spin degree of freedom into a hydrodynamic theory. The relativistic spin hydrodynamics have the conservation equations for energy-momentum tensor, currents and total angular momentum. In this article, we give an overview of the recent progresses of the relativistic spin hydrodynamics. We focus on the following topics: 1) The derivation of the relativistic spin hydrodynamic equations, including the phenomenological approach, the effective theory method, and the kinetic approach, 2) Some special properties of spin hydrodynamics, especially the asymmetric energy-momentum tensor and the pseudogauge transformation, and 3) The analytical solutions to the relativistic spin hydrodynamics for systems under Bjorken and Gubser expansion.