Graphene and graphene-like two-dimensional (2D) materials have attracted much attention due to its extraordinary electronic and optical properties, which accommodate a large potential In optoelectronic applications such as photodetection. However, although much progress has been made, many challenges exist in fundamental and practical aspects hindering graphene and graphene-like 2D materials from photodetector and other photonic and optoelectronic applications. Here, we review the recent progress in photodetection based on graphene and graphene-like 2D materials and start with the summary of some most important physical mechanisms, including photoelectric, photo-thermoelectric, and photo-bolometric regimes. Then methodology-level discussions are given from viewpoints of state-of-the-art designs in device geometry and materials. It is worth emphasizing that emerging photodetection and photodetectors based on graphene-like 2D materials such as metal chalcogenide nanosheets are reviewed systematically. Finally, we conclude this review in a brief discussion with remaining challenges in photodetection of two-dimensional photonics and optoelectronics (2D POE) and note that complete understandings of 2D materials and 2D POE may inspire solar energy conversion and other new applications.