Due to its special optical properties the surface plasmon polariton (SPP) has been applied to many fields such as chemistry, biology, communication, nano energy. The more in-depth researches on plasmonic band structures can conduce to understanding more the properties of plasmonic micro- and nano-structures. In this review, we first introduce some metal structures which have plasmonic band structures. Then, we review some unique properties of plasmonic band structures including bound state in the continuum, waveguide, complete band gap, topology, etc. Based on the above properties, the plasmonic applications are introduced. Finally, we briefly introduce the band structures of graphene-based plasmonics and its applications.