Offshore　floating　platforms　(OFPs)　are　widely　used　in　offshore　industries　for　oil　exploration　and　exploitation.　Harsh　environmental　loads　such　as　wind　and　sea　waves　may　induce　excessive　vibrations　to　OFPs　and　endanger　their　safety.　Inerter,　which　can　produce　a　considerable　apparent　mass　that　is　much　larger　than　its　physical　mass　through　an　amplifying　mechanism　by　translating　the　linear　motion　into　high-speed　rotational　motion,　has　been　adopted　for　structural　vibration　control　recently.　The　authors　proposed　using　inerter　for　OFP　vibration　control.　This　paper　will　summarize　the　corresponding　research　works　carried　out　by　the　authors　in　this　area.　In　particular,　analytical　and　experimental　studies　will　be　reported　in　detail.　©　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.　2024.