Perovskite is a promising candidate for photodetector applications owing to its outstanding optical and electrical characteristics, such as a tunable bandgap, a high absorption co-efficiency, and a long and balanced carrier diffusion length. Perovskite crystals are diverse in their morphologies, which include micro and nano crystalline films, single crystalline bulks, and single crystalline nanocrystals. In this study, the photodetectors composed of perovskite crystals with different morphologies based on the principles of photoconductive, photovoltaic, field effect transistor, and photomultiplication are reviewed, which reveal different characteristics in terms of responsivity, detectivity, and response speed. The research progress of perovskite photodetectors is summarized in each of the aspects of flexibility, narrow band response, self-powered photodetection, and patterned array. A future prospect of perovskite photodetectors is also discussed.