Flexible photodetectors have attracted a great deal of research interest in recent years due to their great possibilities for application in a variety of emerging areas such as flexible, stretchable, implantable, portable, wearable and printed electronics and optoelectronics. Novel functional materials, including materials with zero‐dimensional (0D) and one‐dimensional (1D) inorganic nanostructures, two‐dimensional (2D) layered materials, organic semiconductors and perovskite materials, exhibit appealing electrical and optoelectrical properties, as well as outstanding mechanical flexibility, and have been widely studied as building blocks in cost‐effective flexible photodetection. Here, we comprehensively review the outstanding performance of flexible photodetectors made from these novel functional materials reported in recent years. The photoresponse characteristics and flexibility of the devices will be discussed systematically. Summaries and challenges are provided to guide future directions of this vital research field. Flexible photodetectors are of great importance in next‐generation optoelectronics and can provide a number of new functionalities towards some practical applications. The development of flexible photodetectors based on various novel functional materials are reviewed. Their photoresponse properties and mechanical flexibility are systematically discussed. Conclusions on the current techniques and future challenges are presented.