Graphene oxide and graphene quantum dots are attractive fluorophores, which are inexpensive, non-toxic, photo-stable, water-soluble, biocompatible and environmentally friendly. They find extensive applications in fluorescent biosensors and chemi-sensors, in which they either serve as fluorophores or quenchers. As fluorophores, they display the tunable photoluminescence emission and the “Giant Red-Edge Effect”. As quenchers, they exhibit a remarkable quenching efficiency via either electron transfer or Förster resonance energy transfer (FRET) process. In this review article, the origin of fluorescence and the mechanism of excitation wavelength-dependent fluorescence of graphene oxide and graphene quantum dots are discussed. The sensor design strategies based on graphene oxide and graphene quantum dots are presented. The applications of such sensors in health care, environment, agriculture and food safety are highlighted.