Because the Oort Cloud is cold, remote, and relatively sparsely populated, it was long believed to act as a perfect storage environment for comets. However, over the past decade a series of physical processes have been shown to modify the outer layers of cometary nuclei while they are in the Cloud. These are:(i) irradiation by high energy photons, cosmic rays, and energetic solar particles from the solar wind, (ii) heating by luminous passing stars and supernovae (SN), (iii) erosive interactions with grains in the interstellar medium (ISM), (iv) regolith gardening by debris impacts, and (v) catastrophic collisions among the population. We review the effects and potential observables created by of each process individually, and then comment on the net effects of these processes acting in combination. We further discuss the relative importance of each process with regard to comets stored in the Edgeworth-Kuiper Belt and the Oort Cloud.