Abstract: The theory of radiation hydrodynamics finds a wide range of application, including supernova explosions and the physics of laser fusion. In this talk we shall introduce the general equations of radiation hydrodynamics which are a nonlinear hyperbolic-transport coupled system. Then, we describe some approximate models such as the diffusion approximation and the equilibrium diffusion approximation. Recent mathematical results such as the existence, development of singularities, stability for radiation hydrodynamics will be described, and the mathematical difficulties will also be discussed.