Graphene and graphene-based materials exhibit exceptional optical and electrical properties with great promise for novel applications in light detection. However, several challenges prevent the full exploitation of these properties in commercial devices. Such challenges include the limited linear dynamic range (LDR) of graphene-based photodetectors, the lack of efficient generation and extraction of photoexcited charges, the smearing of photoactive junctions due to hot-carriers effects, large-scale fabrication and ultimately the environmental stability of the constituent materials. In order to overcome the aforementioned limits, different approaches to tune the properties of graphene have been explored. A new class of graphene-based devices has emerged where chemical functionalisation, hybridisation with light-sensitising materials and the formation of heterostructures with other 2D materials have led to improved performance, stability or versatility. For example, intercalation of graphene with FeCl$_3$ is highly stable in ambient conditions and can be used to define photo-active junctions characterized by an unprecedented LDR while graphene oxide (GO) is a very scalable and versatile material which supports the photodetection from UV to THz frequencies. Nanoparticles and quantum dots have been used to enhance the absorption of pristine graphene and to enable high gain thanks to the photogating effect. In the same way, hybrid detectors made from stacked sequences of graphene and layered transition-metal dichalcogenides enabled a class of detectors with high gain and responsivity. In this work we will review the performance and advances in functionalised graphene and hybrid photodetectors, with particular focus on the physical mechanisms governing the photoresponse in these materials, their performance and possible future paths of investigation.