The mechanical properties of organic semiconductors and the mechanical failure mechanisms of devices play critical roles in the yield of modules in roll-to-roll manufacturing and the operational stability of organic solar cells (OSCs) in portable and outdoor applications. This paper begins by reviewing the mechanical properties—principally stiffness and brittleness—of pure films of organic semiconductors. It identifies several determinants of the mechanical properties, including molecular structures, polymorphism, and microstructure and texture. Next, a discussion of the mechanical properties of polymer–fullerene bulk heterojunction blends reveals the strong influence of the size and purity of the fullerenes, the effect of processing additives as plasticizers, and the details of molecular mixing—i.e., the extent of intercalation of fullerene molecules between the side chains of the polymer. Mechanical strain in principle affects the photovoltaic output of devices in several ways, from strain-evolved changes in alignment of chains, degree of crystallinity, and orientation of texture, to debonding, cohesive failure, and cracking, which dominate changes in the high-strain regime. These conclusions highlight the importance of mechanical properties and mechanical effects on the viability of OSCs during manufacture and in operational environments. The review—whose focus is on molecular and microstructural determinants of mechanical properties—concludes by suggesting several potential routes to maximize both mechanical resilience and photovoltaic performance for improving the lifetime of devices in the near term and enabling devices that require extreme deformation (i.e., stretchability and ultra-flexibility) in the future.