Biohybrid micro- and nanorobots are integrated tiny machines from biological components and artificial components. They can possess the advantages of onboard actuation, sensing, control, and implementation of multiple medical tasks such as targeted drug delivery, single-cell manipulation, and cell microsurgery. This review paper is to give an overview of biohybrid micro- and nanorobots for smart drug delivery applications. First, a wide range of biohybrid micro- and nanorobots comprising different biological components are reviewed in detail. Subsequently, the applications of biohybrid micro- and nanorobots for active drug delivery are introduced to demonstrate how such biohybrid micro- and nanorobots are being exploited in the field of medicine and healthcare. Lastly, key challenges to be overcome are discussed to pave the way for the clinical translation and application of the biohybrid micro- and nanorobots.