Antibiotic resistance has become one of the greatest challenges for modern medicine, and new approaches for the treatment of bacterial infections are urgently needed to avoid widespread vulnerability again to infections that have so far been easily treatable with existing drugs. Among the many approaches investigated to overcome this challenge is the use of engineered nanostructures for the precise and targeted delivery of existing antimicrobial agents in a fashion that will potentiate their effect. This idea leans on lessons learned from pioneering research in cancer, where the targeted delivery of anti-cancer drugs to mammalian cells has been a topic for some time. In particular, new research has demonstrated that nanomaterials can be functionalised with active antimicrobials and, in some cases, with targeting molecules that potentiate the efficiency of the antimicrobials. In this mini-review, we summarise results that demonstrate the potential for nanoparticles, dendrimers and DNA nanostructures for use in antimicrobial delivery. We consider material aspects of the delivery vehicles and ways in which they can be functionalised with antibiotics and antimicrobial peptides, and we review evidence for their efficacy to kill bacteria both in vitro and in vivo. We also discuss the advantages and limitations of these materials and highlight the benefits of DNA nanostructures specifically for their versatile potential in the present context.