While the field of perovskite-based optoelectronics has mostly been dominated by photovoltaics, light-emitting diodes, and transistors, semiconducting properties peculiar to perovskites make them interesting candidates for innovative and disruptive applications in light signal detection. Perovskites combine effective light absorption in the broadband range with good photo-generation yield and high charge carrier mobility, a combination that provides promising potential for exploiting sensitive and fast photodetectors that are targeted for image sensing, optical communication, environmental monitoring or chemical/biological detection. Currently, organic-inorganic hybrid and all-inorganic halide perovskites with controlled morphologies of polycrystalline thin films, nano-particles/wires/sheets, and bulk single crystals have shown key figure-of-merit features in terms of their responsivity, detectivity, noise equivalent power, linear dynamic range, and response speed. The sensing region has been covered from ultraviolet-visible-near infrared (UV-Vis-NIR) to gamma photons based on two- or three-terminal device architectures. Diverse photoactive materials and devices with superior optoelectronic performances have stimulated attention from researchers in multidisciplinary areas. In this review, we provide a comprehensive overview of the recent progress of perovskite-based photodetectors focusing on versatile compositions, structures, and morphologies of constituent materials, and diverse device architectures toward the superior performance metrics. Combining the advantages of both organic semiconductors (facile solution processability) and inorganic semiconductors (high charge carrier mobility), perovskites are expected to replace commercial silicon for future photodetection applications.