Non-fullerene electron acceptors (NFAs) are recognized as "rising star" in recent years in the organic solar cells (OSCs) community. In contrast to the traditional fullerene electron acceptors, NFAs promise superior feasibility in molecular design with tunable optoelectronic properties, experiencing unprecedented development in the last 5 years with maximum achievable power conversion efficiencies over 18% are acquired in NFA based OSCs. Nevertheless, the stability of NFAs and their OSCs is still problematic and not well understood, and is regarded as the bottleneck toward the commercialization of NFA based OSCs. In this review, recent advances and current understanding of the stability of NFAs and their corresponding OSCs are presented. Specifically, three key factors, including chemical-, photon-, and thermal-, induced degradations in NFAs are analyzed and summarized, with approaches to enhance the stability suggested. This is followed by the discussion of shelf and operational stability of NFA based OSCs, with highlights of operational stabilities in inert, ambient, indoor, and outdoor conditions. It is envisaged that operational lifetime of over 20 years in real world is achievable via the joint efforts from material design, morphology control, interfacial engineering, and encapsulation technology.