This thesis details the development of the radiation transport code torus for radiation hydrodynamic applications and its subsequent use in investigating problems regarding radiative feedback. The code couples Monte Carlo photoionization with grid-based hydrodynamics and has the advantage that all of the features available to a dedicated radiation transport code are at its disposal in RHD applications. I discuss the development of the code, including the hydrodynamics scheme, the adaptive mesh refinement (AMR) framework and the coupling of radiation transport with hydrodynamics. Extensive testing of the resulting code is also presented. The main application involves the study of radiatively driven implosion (RDI), a mechanism where the expanding ionized region about a massive star impacts nearby clumps, potentially triggering star formation. Firstly I investigate the way in which the radiation field is treated, isolating the relative impacts of polychromatic and diffuse field radiation on the evolution of radiation hydrodynamic RDI models. I also produce synthetic SEDs, radio, Hα and forbidden line images of the bright rimmed clouds (BRCs) resulting from the RDI models, on which I perform standard diagnostics that are used by observers to obtain the cloud conditions. I test the accuracy of the diagnostics and show that considering the pressure difference between the neutral cloud and surrounding ionized layer can be used to infer whether or not RDI is occurring. Finally I use more synthetic observations to investigate the accuracy of molecular line diagnostics and the nature of line profiles of BRCs. I show that the previously unexplained lack of dominant blue-asymmetry (a blue-asymmetry is the expected signature of a collapsing cloud) in the line profiles of BRCs can be explained by the shell of material, swept up by the expanding ionized region, that drives into the cloud. The work in this thesis combines to help resolve the difficulties in understanding radiative feedback, which is a non–linear process that happens on small astrophysical timescales, by improving numerical models and the way in which they are compared with observations.