Low-dimensional inorganic nanostructures such as quantum dots as well as one- and two-dimensional nanostructures are widely studied and already used in high-performance infrared photodetectors. These structures feature large surface-to-volume ratios, tunable light absorption, and electron-limiting effects. This article reviews the state-of-the-art research of low-dimensional inorganic nanostructures and their application for infrared photodetection. Thanks to nano-structuring, a narrow bandgap, hybrid systems, surface-plasmon resonance, and doping, many common semiconductors have the potential to be used for infrared detection. The basic approaches towards infrared detection are summarized. Furthermore, a selection of very important and special nanostructured materials and their remarkable infrared-detection properties are introduced (e.g., black phosphorus, graphene-based, MoX₂-based, Ⅲ-Ⅶ group). Each section in this review describes the corresponding photosensitive properties in detail. The article concludes with an outlook of anticipated future developments in the field.