Radio galaxies, active galactic nuclei with misaligned relativistic jets and large diffuse extended lobe structures, are home to radiative processes which are still not well understood. In this thesis, I describe my use of gamma-ray photon data from the Fermi Large Area Telescope to investigate these radiative processes in the case of two radio galaxies, Fornax A and Centaurus A. I describe my discovery of the spatially extended nature of the gamma-ray emission from Fornax A and my observation of a gamma-ray intensity which is not consistent with the predicted process of stray energetic electrons inverse-Compton scattering with extragalactic background light photons. I describe how I positively identified a new gamma-ray spectral component from the core region of Centaurus A jointly with data from the High Energy Stereoscopic System and how the spectral component can be explained by the addition of a second hidden zone of synchrotron self-Compton emission. I describe my discovery of fine filamentary sub-structures in the gamma-ray lobes of Centaurus A using a new imaging technique which I created, mapping out the unexpected gamma-ray emission farther from the assumed central engine than we have observed in radio. I discuss how my observations of the Centaurus A lobes suggest local re-acceleration or channels of negligible magnetic field allowing long distance high energy particle paths.