Bismuth-based compounds have recently gained interest as solar absorbers with the potential to have low toxicity, be efficient in devices, and be processable using facile methods. We review recent theoretical and experimental investigations into bismuth-based compounds, which shape our understanding of their photovoltaic potential, with particular focus on their defect-tolerance. We also review the processing methods that have been used to control the structural and optoelectronic properties of single crystals and thin films. Additionally, we discuss the key factors limiting their device performance, as well as the future steps needed to ultimately realize these new materials for commercial applications.