Graphene-based nanosheets (GNS), including graphenes, graphene oxides and reduced graphene oxides, have properties suitable for delivery of various molecules. With their two-dimensional structures, GNS provide relatively high surface areas and capacity for non-covalent π-π stacking and hydrophobic interactions with various drug molecules. Currently, GNS-based delivery applications extend to chemotherapeutics as well as biological drugs, including nucleic acid drugs, proteins, and peptides. Surfaces of GNS have been modified with various polymers, such as polyethylene glycol and biopolymers, which enhance biocompatibility and increase drug loading. Anticancer drugs are prominent among chemotherapeutic agents tested, and have been loaded onto GNS with relatively high loading capacities compared with other nanocarriers. For enhanced distribution to specific tissues, GNS have been covalently or non-covalently modified with targeting ligands, including folic acid, transferrins, and others. In this review, we cover the current status of GNS for delivery of anticancer chemotherapeutics and biological drugs, with a focus on nucleic acid drugs. Remaining challenges for the application of GNS for drug-delivery systems and future perspectives are also addressed.