One of the most violent ways a supermassive black hole can interact with its surroundings is by tearing apart stars that pass too close to it. The resulting debris streams can collide, shock, and accrete onto the black hole, giving rise to a flare of light that tends to peak on a timescale of weeks to months. Such flares, labeled tidal disruption events (TDEs), were first predicted decades ago, but it is only in the last few years that they have been observed systematically at a variety of wavelengths. These observations have led to a number of puzzles, including the need to explain why some TDEs are bright at optical/UV wavelengths, why are hydrogen emission lines in the optical spectrum often so weak compared to those of helium, and why the color of the optical/UV emission does not appear to evolve significantly over time. In this talk I will present radiative transfer calculations to address these questions. We track the reprocessing of accretion luminosity from a supermassive black hole as the light travels through an extended, optically thick, spherical envelope composed of hydrogen, helium, and oxygen from the disrupted star. The steady-state radiative transfer equation is coupled to a solver for the atomic level populations and ionization states that does not assume local thermodynamic equilibrium. Our calculations show how the hydrogen optical emission lines can become more effectively optically thick than their helium counterparts, causing them to remain hidden even in the disruption of a hydrogen-rich star. More generally, variations in the structure of the reprocessing material can give rise to a variety of hydrogen-to-helium line ratios, as has been seen in recent observations. We also determine the amount of material necessary to transfer enough radiative energy from x-ray to optical wavelengths to match what is observed, and we demonstrate how the partial absorption of ionizing radiation can give rise to events simultaneously observed in x-rays and in the optical.