Two-dimensional (2D) materials have been widely used in photodetectors owing to their diverse advantages in device fabrication and manipulation, such as integration flexibility, availability of optical operation through an ultrabroad wavelength band, fulfilling of photonic demands at low cost, and applicability in photodetection with high-performance. Recently, transition metal dichalcogenides (TMDCs), black phosphorus (BP), III-V materials, heterostructure materials, and graphene have emerged at the forefront as intriguing basics for optoelectronic applications in the field of photodetection. The versatility of photonic systems composed of these materials enables their wide range of applications, including facilitation of chemical reactions, speeding-up of responses, and ultrasensitive light detection in the ultraviolet (UV), visible, mid-infrared (MIR), and far-infrared (FIR) ranges. This review provides an overview, evaluation, recent advancements as well as a description of the innovations of the past few years for state-of-the-art photodetectors based on two-dimensional materials in the wavelength range from UV to IR, and on the combinations of different two-dimensional crystals with other nanomaterials that are appealing for a variety of photonic applications. The device setup, materials synthesis, operating methods, and performance metrics for currently utilized photodetectors, along with device performance enhancement factors, are summarized.