In recent years, the rapid progress of metal halide perovskite solar cells has been witnessed by the rocketing power conversion efficiency. In addition, perovskites have opened up a great opportunity for high performance photodetectors (PDs), due to their attractive optical and electrical properties. This review summarizes the latest progress of perovskite-based PDs, aiming to give a comprehensive understanding of the material design and device engineering in perovskite PDs. To begin with, the performance parameters and device configurations of perovskite PDs are introduced, which are the basis for the next discussion. Next, various PDs based on perovskites in different morphologies are discussed from two aspects:the preparation method, and device performance. Then, several device engineering strategies to enhance the performance of perovskite-based PDs are highlighted, followed by the introduction of flexible and narrow-band perovskite PDs. Finally, key issues and major challenges of perovskite PDs that need to be addressed in the future are outlined.