In the last decade, optoelectronic devices based on organic‐inorganic hybrid perovskite (OIHP) materials, which have unique advantages of direct bandgap, large absorption coefficient, low density of defects, long charge carrier lifetime, diffusion length, and solution processability, have traveled with traditional inorganic semiconductor devices. The state‐of‐the‐art OIHP photodetectors have contributed a comparable performance with Si and III‐V compound semiconductor based photodetectors. Large amount of efforts have been focused on improving sensitivity, broadening detection spectra, enlarging linear dynamic range. However, few reports emphasized the important parameter of response speed. In this review, we summarize the progress and applications of OIHP photodetectors with fast response. Based on photovoltaic and photoconductive‐type OIHP photodetectors, the working principle and key factors on determining response speed are systematically mentioned. Then, the research progress of response speed, which is composed of resistance‐capacitance (RC) time constant and charge carrier transit time is discussed in detail. Subsequently, considering the intrinsic flexibility of perovskite materials, we briefly discuss the flexible photodetectors. Finally, an outlook and potential rules for designing fast‐response OIHP photodetectors are further proposed.