Aqueous organic redox flow batteries (RFBs) could enable widespread integration of renewable energy, but only if costs are sufficiently low. Because the levelized cost of storage for an RFB is a function of electrolyte lifetime, understanding and improving the chemical stability of active reactants in RFBs is a critical research challenge. We review known or hypothesized molecular decomposition mechanisms for all five classes of aqueous redox-active organics and organometallics for which cycling lifetime results have been reported: quinones, viologens, aza-aromatics, iron coordination complexes, and nitroxide radicals. We collect, analyze, and compare capacity fade rates from all aqueous organic electrolytes that have been utilized in the capacity-limiting side of flow or hybrid flow/nonflow cells, noting also their redox potentials and demonstrated concentrations of transferrable electrons. We categorize capacity fade rates as being "high" (>1%/day), "moderate" (0.1-1%/day), "low" (0.02-0.1%/day), and "extremely low" (≤0.02%/day) and discuss the degree to which the fade rates have been linked to decomposition mechanisms. Capacity fade is observed to be time-denominated rather than cycle-denominated, with a temporal rate that can depend on molecular concentrations and electrolyte state of charge through, e.g., bimolecular decomposition mechanisms. We then review measurement methods for capacity fade rate and find that simple galvanostatic charge-discharge cycling is inadequate for assessing capacity fade when fade rates are low or extremely low and recommend refining methods to include potential holds for accurately assessing molecular lifetimes under such circumstances. We consider separately symmetric cell cycling results, the interpretation of which is simplified by the absence of a different counter-electrolyte. We point out the chemistries with low or extremely low established fade rates that also exhibit open circuit potentials of 1.0 V or higher and transferrable electron concentrations of 1.0 M or higher, which are promising performance characteristics for RFB commercialization. We point out important directions for future research.