Organic solar cells (OSCs) are lightweight, have adaptable colors, and can be produced in low‐cost procedures on transparent and flexible surfaces. This makes them attractive for markets in which other technologies cannot compete, for example in architectural and consumer product integration. However, both efficiencies and long term operational stability of OSCs do not yet meet the standards set by their inorganic counterparts. This review compiles the growing knowledge about how nanostructured carbon materials, such as fullerenes and carbon nanotubes, decisively influence the operational stability of organic photovoltaics. Firstly, important degradation pathways are introduced and a differential detection scheme is set up to find the dominant loss channel by means of state‐of‐the‐art characterization methods. Then, fullerenes ability to both stabilize and destabilize the donor polymer against photooxidation via different mechanisms (e.g., inner filter effect or radical scavenging) is examined in detail. The “burn‐in” problem, an initial rapid efficiency loss in PC₆₀BM‐based OSCs, is shown to derive from light‐induced PC₆₀BM dimerization, an effect that can also be positively exploited to reduce thermal degradation. Finally, thermal stabilization via additional approaches involving the fullerene derivative, such as crosslinking or incorporation into block copolymers, is presented.