Future electronics will need to be mechanically flexible and stretchable in order to enable the development of lightweight and conformal applications. In contrast, photodetectors, an integral component of electronic devices, remain rigid, which prevents their integration into everyday life applications. In recent years, significant efforts have been made to overcome the limitations of conventional rigid photodetectors, particularly their low mechanical deformability. One of the most promising routes toward facilitating the fabrication of flexible photodetectors is to replace conventional optoelectronic materials with nanomaterials or organic materials that are intrinsically flexible. Compared with other functional materials, organic polymers and molecules have attracted more attention for photodetection applications due to their excellent photodetection performance, cost-effective solution-fabrication capability, flexible design, and adaptable manufacturing processes. This article comprehensively discusses recent advances in flexible organic photodetectors in terms of optoelectronic, mechanical properties, and hybridization with other material classes. Furthermore, flexible organic photodetector applications in health-monitoring sensors, X-ray detection, and imager devices have been surveyed.