In one embodiment, the present invention relates to a method for producing polymer nanostructures, the method comprising the steps of: forming at least one nanostructure substrate, web, membrane or mat; exposing the at least one nanostructure substrate, web, membrane or mat to at least one monomer composition, where the at least one monomer composition is in a vapor phase and the at least one monomer composition is deposited on the surface of and/or within the at least one nanostructure substrate, web, membrane or mat; and subjecting the at least one exposed nanostructure substrate, web, membrane or mat to conditions suitable to polymerize the at least one monomer composition, thereby yielding polymer nanostructures where the polymer nanostructures are formed on and/or in the nanostructure substrate, web, membrane or mat.