Nanoscale assemblies are a unique class of materials, which can be synthesized from inorganic, polymeric or biological building blocks. The multitude of applications of this class of materials ranges from solar and electrical to uses in food, cosmetics and medicine. In this review, we initially highlight characteristic features of polymeric nanoscale assemblies as well as those built from biological units (lipids, nucleic acids and proteins). We give special consideration to protein nanoassemblies found in nature such as ferritin protein cages, bacterial microcompartments and vaults found in eukaryotic cells and designed protein nanoassemblies, such as peptide nanofibres and peptide nanotubes. Next, we focus on biomedical applications of these nanoscale assemblies, such as cell targeting, drug delivery, bioimaging and vaccine development. In the vaccine development section, we report in more detail the use of virus-like particles and self-assembling polypeptide nanoparticles as new vaccine delivery platforms.