Disclosed herein are nanostructures and their use, where the nanostructures include (a) a plurality of first assemblies, each first assembly comprising a plurality of identical first polypeptides; (b) a plurality of second assemblies, each second assembly comprising a plurality of identical second polypeptides, wherein the second polypeptide differs from the first polypeptide; wherein the plurality of first assemblies non-covalently interact with the plurality of second assemblies to form a nanostructures; and wherein the nanostructure displays multiple copies of one or more paramyxovirus and/or pneumovirus F proteins or antigenic fragments thereof, on an exterior of the nanostructure.