Nanocarbon allotropes (NCAs), including zero-dimensional carbon dots (CDs), one-dimensional carbon nanotubes (CNTs) and two-dimensional graphene, exhibit exceptional material properties, such as unique electrical/thermal conductivity, biocompatibility and high quenching efficiency, that make them well suited for both electrical/electrochemical and optical sensors/biosensors alike. In particular, these material properties have been exploited to significantly enhance the transduction of biorecognition events in fluorescence-based biosensing involving Förster resonant energy transfer (FRET). This review analyzes current advances in sensors and biosensors that utilize graphene, CNTs or CDs as the platform in optical sensors and biosensors. Widely utilized synthesis/fabrication techniques, intrinsic material properties and current research examples of such nanocarbon, FRET-based sensors/biosensors are illustrated. The future outlook and challenges for the research field are also detailed.