Nanobioconjugates are nanoscale drug delivery vehicles that have been conjugated to or decorated with biologically active targeting ligands. These targeting ligands can be antibodies, peptides, aptamers, or small molecules such as vitamins or hormones. Most research studies in this field have been devoted to targeting cancer. Moreover, the nanostructures can be designed with an additional level of targeting by being designed to be stimulus-responsive or "smart" by a judicious choice of materials to be incorporated into the hybrid nanostructures. This stimulus could be an acidic pH, raised temperature, enzyme, ultrasound, redox potential, an externally applied magnetic field, or laser irradiation. In this case, the smart capability can increase the accumulation at the tumor site or the on-demand drug release, while the ligand ensures selective binding to the tumor cells. The present review highlights some interesting studies classified according to the nanostructure material. These materials include natural substances (polysaccharides), multi-walled carbon nanotubes (and halloysite nanotubes), metal-organic frameworks and covalent-organic frameworks, metal nanoparticles (gold and silver), and polymeric micelles.