Colloidal quantum dot solar cells (QDSCs) are promising candidates amongst third generation photovoltaics due to their bandgap tunability, facile low-temperature ink processing, strong visible-to-infrared absorption, and potential for multiple-exciton generation. An unprecedented increase in power conversion efficiency is reported for different types of QDSCs in the last few years, making them appealing for large-scale fabrication. The stability of QDSCs, however, still remains inadequate for industrial application, especially when they are operated under a sun-like illumination in an ambient atmosphere. This review focuses on three classes of QDs (lead chalcogenides, lead halide perovskites, and lead-free QDs) and considers the current understanding of their degradation mechanisms. For each material class, strategies for stability improvement are discussed, both from materials science and device engineering perspectives. This paper concludes by suggesting a methodology for characterizing the QDSCs’ stability which would standardize the results obtained by researchers worldwide.