Vibration　damping　is　very　important　to　improve　dynamic　behavior　of　composite　structures.　There　is　a　strong　need　for　information　on　damping　research　in　design　optimization　of　composite　structures.　In　this　paper,　the　status　of　research　on　damping　in　fiber-reinforced　composite　materials　and　structure　has　been　reviewed.　The　content　can　be　divided　into　three　parts,　such　as　damping　mechanisms,　modeling　of　damping　and　enhancement　of　damping.　At　last,　the　recommendations　regarding　future　research　have　also　been　offered.