The development of sophisticated multi-dimensional self-gravitational radiation hydrodynamic codes in astrophysics has brought important focus onto the verification and the validation of the physical models within the codes as well the integrated codes themselves. In this lecture I shall discuss new methodologies we have developed embodying high order accurate techniques to solve the three-dimensional equations of self-gravitational radiation hydrodynamics using adaptive mesh refinement. I will discuss the astrophysics of strongly coupled radiation hydrodynamic flows in two problems of great current interest; the development of photon bubble instabilities in neutron star atmospheres and accretion disks and the problem of high mass star formation. I will then discuss various approaches to the verification of the equations and the algorithms including the testing of hydrodynamics, radiation transport and coupled radiation hydrodynamics. I shall then describe laboratory experiments we have conducted to validate the component physics of both the radiation and the hydrodynamics in the code and novel work I am engaged in to design an experiment on ultraintense petawatt lasers to simulate for the first time, photon bubbles in the laboratory.