This thesis explores the calculations of radiative opacity and its use in modelling radiation transport within high energy density environments, such as those found in laboratory astrophysics and inertial confinement fusion research. Recent work has demonstrated that there may be substantial shortcomings in our current theories of opacity, which motivates a deep consideration of how current opacities are determined and how they are implemented into large scale simulations. Notably, we derive multiplicative correction factors which counteract inaccuracies that may arise due to differences in radiation and electron temperature when calculating such parameters in three-temperature radiation transport algorithms, which is relevant to modelling volume ignition experiments. The Multigroup Diffusion Algorithm for Radiation Transport (M-DART) is then introduced, which was written solely by the author for the intended purpose of providing a fast platform to model supersonic Marshak wave propagation. The M-DART algorithm is then utilised to highlight the necessary convergence steps in using multigroup diffusion algorithms to model radiation wave experiments, which probe the propagation of a Marshak wave through material. We find that computational parameters, such as poor group boundary positions, can lead to large changes in the properties of a Marshak wave, resulting in signatures which cannot be attributed solely to physical effects. M-DART is also used to explore the physical sensitivities present in a recent AWE-NIF shot which probed iron opacity under solar-relevant conditions. In doing this, an extensive insight into the important parameters which must be constrained in such an experiment are identified and analysed meticulously, providing a preliminary investigation into the feasibility of using modern M-DART along with the fast opacity code IMP and statistical methods to enhance findings within the experimental campaign. Finally, an investigation into line broadening due to intense radiation fields is documented and demonstrates that there may exist a region in temperature-density space where the broadening of spectral lines due to the presence of a radiation field could become dominant over Stark broadening and neutral broadening, which would have implications for the calculations of opacity and radiation transport in white dwarf atmospheres. Open Access