Modern medicine has relied heavily on the availability of effective antibiotics to manage infections and enable invasive surgery. With the emergence of antibiotic-resistant bacteria, novel approaches are necessary to prevent the formation of biofilms on sensitive surfaces such as medical implants. Advances in nanotechnology have resulted in novel materials and the ability to create novel surface topographies. This review article provides an overview of advances in the fabrication of antimicrobial nanomaterials that are derived from biological polymers or that rely on the incorporation of natural compounds with antimicrobial activity in nanofibers made from synthetic materials. The availability of these novel materials will contribute to ensuring that the current level of medical care can be maintained as more bacteria are expected to develop resistance against existing antibiotics.