Fullerenes presents a unified introduction to the multidisciplinary world of fullerene nanoscience based on a single paradigm of concepts, terminology, and ideas. It uses a computational platform to embrace two distinguishing fullerene features: odd electrons and exclusive donor-acceptor abilities. The author showcases fullerene nanoscience from a computational viewpoint, intertwining theory and experiment to elucidate key concepts in fullerene science and future avenues of exploration. She uses fullerene membership in sp2 nanocarbon nanoscience to demonstrate the intimate similarity in the behavior of fullerene, carbon nanotubes, and graphene.