Graphene and its derivatives having at least one dimension in nanoscale range have attracted tremendous attention in recent years due to their unique electronic, optical, chemical, and mechanical properties. This chapter is about graphene quantum dots (GQDs) that are zero-dimensional graphene derivatives with one to few layers of graphene sheet having size range less than 20nm. This chapter is an overview of synthesis of GQDs by top-down and bottom-up approaches, as well as detailed methods of synthesis of GQDs by acidic oxidation of carbon fibers. Owing to their extremely small size, quantum confinement, edge effect, biocompatibility, low toxicity, photostability as well as water solubility they are excellent candidates for understanding biological systems and cellular processes at the molecular scale. These are also suitable nanomaterials to replace inorganic semiconducting nanoparticles (e.g., CdS, CdSe, ZnS, and Si) which are toxic to biological systems.