Two-dimensional (2D) materials, which have a thickness on the atomic scale, have attracted wide attention due to their unique physical and chemical properties. Because of their high carrier mobility, strong light-matter interaction, and anisotropic electronic/optical properties, etc., 2D materials show promising applications in optoelectronics. Among the 2D materials, narrow band gap semiconductors, such as black phosphorus, black arsenic phosphorus, etc., have shown huge potential in infrared photodetectors and have become star materials in infrared photodetectors. In this review, recent advances in 2D materials in infrared photodetectors are introduced, with an emphasis on photodetectors depending on the inner photoelectronic effect. First, the background of 2D materials is introduced. Then, the key parameters for infrared photodetectors, such as the responsivity, quantum efficiency, specific detectivity, and response speed, are listed. This is followed by the presentation of the recent advances of 2D materials in infrared photodetectors, which is divided into three parts: single component 2D material photodetectors, heterostructure infrared photodetectors, and waveguide photodetectors. Finally, a summary and outlook are provided for a guideline. We hope the present review will show the huge potential of 2D materials in infrared photodetectors and attract more exciting work on infrared photodetectors based on 2D materials in the future.