Radiation hydrodynamics describes the interactions between matter and radiation which affect the thermodynamic states and the dynamic flow characteristics of the matter-radiation system. Its application areas are mainly in high-temperature hydrodynamics, including astrophysics, reentry vehicles fusion physics and inertial confinement fusion. In this talk, we will discuss the methodology to construct fully explicit and implicit-explicit (IMEX) high order Lagrangian schemes solving the one-dimensional radiative hydrodynamics equations in the equilibrium diffusion limit respectively, which can be used to simulate multi-material problems with the coupling of radiation and hydrodynamics. The schemes can maintain conservation and uniformly high order accuracy both in space and time. The issue of positivity-preserving for the explicit high order Lagrangian scheme is also discussed. Various numerical tests for the high order Lagrangian schemes are provided to demonstrate the desired properties of the schemes such as high order accuracy, non-oscillation, and positivity-preserving.