Structure　vibration　control　using　shape　memory　alloy(SMA)　has　been　widely　considered.　Currently,　the　SMA　is　developing　pretty　fast　while　there　are　huge　differences　among　various　families　of　SMAs.　Therefore,　the　appropriate　selection　of　the　SMAs　in　structure　vibration　control　is　quite　essential.　In　the　paper,　the　developments　of　SMAs　were　reviewed　with　respect　to　mechanical　properties,　thermal　control　properties,　cost　and　service　safety,　etc.　Then,　the　structure　passive　control,　structure　active　control　and　structure　semi-active　control　using　SMA　were　summarized　and　the　advantages,　challenges　and　potentials　of　different　families　of　SMAs　in　these　applications　were　discussed.　The　paper　provides　an　outlook　for　the　applications　of　SMAs　in　civil　engineering　and　points　out　crucial　problems　which　need　to　be　solved　in　future　studies.　©　2019,　Editorial　Office　of　Journal　of　Vibration　and　Shock.　All　right　reserved.