Organic solar cells (OSCs) present some advantages, such as simple preparation, light weight, low cost and large-area flexible fabrication, and have attracted much attention in recent years. Although the power conversion efficiencies have exceeded 10%, the inferior device stability still remains a great challenge. In this review, we summarize the factors limiting the stability of OSCs, such as metastable morphology, diffusion of electrodes and buffer layers, oxygen and water, irradiation, heating and mechanical stress, and survey recent progress in strategies to increase the stability of OSCs, such as material design, device engineering of active layers, employing inverted geometry, optimizing buffer layers, using stable electrodes and encapsulation. Some research areas of device stability that may deserve further attention are also discussed to help readers understand the challenges and opportunities in achieving high efficiency and high stability of OSCs towards future industrial manufacture.