Fluorescence provides a mechanism for achieving contrast in biological imaging that enables investigations of molecular structure, dynamics, and function at high spatial and temporal resolution. Small-molecule organic fluorophores have proven essential for such efforts and are widely used in advanced applications such as single-molecule and super-resolution microscopy. Yet, organic fluorophores, like all fluorescent species, exhibit instabilities in their emission characteristics, including blinking and photobleaching that limit their utility and performance. Here, we review the photophysics and photochemistry of organic fluorophores as they pertain to mitigating such instabilities, with a specific focus on the development of stabilized fluorophores through derivatization. Self-healing organic fluorophores, wherein the triplet state is intramolecularly quenched by a covalently attached protective agent, exhibit markedly improved photostabilities. We discuss the potential for further enhancements towards the goal of developing "ultra-stable" fluorophores spanning the visible spectrum and how such fluorophores are likely to impact the future of single-molecule research.