Two-dimensional layered materials (2DLMs) have attracted a tremendous amount of attention as photodetectors due to their fascinating features, including high potentials in new-generation electronic devices, wide coverage of bandgaps, ability to construct van der Waals heterostructures, extraordinary light-mass interaction, strong mechanical flexibility, and the capability of enabling synthesis of 2D nonlayered materials. Until now, most attention has been focused on the well-known graphene and transition metal dichalcogenides (TMDs). However, a growing number of functional materials (more than 5619) with novel optoelectronic and electronic properties are being re-discovered, thereby widening the horizon of 2D libraries. In addition to showing common features of 2DLMs, these new 2D members may bring new opportunities to their well-known analogues, like wider bandgap coverage, direct bandgaps independence with thickness, higher mechanical flexibility, and new photoresponse phenomena. The impressive results communicated so far testify that they have shown high potentials with photodetections covering THz, IR, visible, and UV ranges with comparable or even higher performances than well-known TMDs. Here, we give a comprehensive review on the state-of-the-art photodetections of two-dimensional materials beyond graphene and TMDs. The review is organized as follows: fundamentals of photoresponse first are discussed, followed by detailed photodetections of new 2D members including both layered and non-layered ones. After that, photodiodes and hybrid structures based on these new 2D materials are summarized. Then, the integration of these 2D materials with flexible substrates is reviewed. Finally, we conclude with the current research status of this area and offer our perspectives on future developments. We hope that, through reading this manuscript, readers will quickly have a comprehensive view on this research area.