Many biologically relevant structures are formed by the self-assembly of identical protein units. Examples include virus capsids or cytoskeleton components. Synthetic biology can harness these bottom-up assemblies and expand their scope for applications in cell biology and biomedicine. Nanobiotechnology and materials science also stand to gain from assemblies with unique nanoscale periodicity. In these disciplines, the soft scaffolds can serve as templates to produce new metallic or inorganic materials of predefined dimensions. This review article describes how the structure and function of biological assemblies has inspired researchers to develop engineered systems with designed properties for new biomolecular applications.