The performance of organic photodetectors is steadily improving, and the specific detectivity, as a key figure of merit, has reached values of 1012–1013 Jones, i.e., comparable to that of silicon diodes but still considerably lower than the intrinsic limit. As with other semiconductor devices, the electrical performance of state‐of‐the art organic photodiodes (OPDs) is presently determined to a high degree by the presence of chemical impurities or structural defects which create carrier trapping states within the bandgap of organic active layer. This review aims to provide a comprehensive and timely account of trap‐assisted charge generation and recombination in OPDs, with emphasis on the impact of these phenomena on photodetector performance parameters such as, noise and dark current density, responsivity, response speed, and ultimately, specific detectivity.