Composite　laminated　structures　have　attracted　considerable　attentions　in　the　field　of　aerospace,　marine,　and　even　renewable　energy　due　to　their　high　stiffness,　strength,　weight　reduction,　fatigue　life,　and　wear　resistance.　Linear　and　nonlinear　vibration　analysis　are　essential　to　predict　the　dynamic　response　for　effective　design　and　structural　integrity　in　various　engineering　applications.　The　key　characteristics　of　the　thin-walled　structures　include　geometrical　and　material　nonlinearity,　temporal　and　spatial　multiscale　feature,　multi-field　coupling　condition　in　complex　operation　environment,　etc.　Significant　progress　has　been　made　in　the　theoretical　modeling,　numerical　simulation,　structural　design,　deformation　mechanism,　and　engineering　application.　This　review　critically　discusses　190　journal　papers　from　the　past　ten　years,　providing　a　comprehensive　exploration　of　the　linear　and　nonlinear　vibrations　of　composite　structures,　which　is　mainly　focused　on　the　analytical　and　numerical　solutions　via　theoretical　derivation,　mesh-based　or　meshless　techniques.　Several　common　composite　materials　and　their　applications　are　described　in　detail.　A　holistic　overview　of　various　homogeneous　modeling　methods　including　analytical　method,　semi-analytical　method,　and　numerical　method　are　provided.　The　theories　and　mathematical　formulations　of　classical　laminate　plate　theory,　shear　deformation　theory,　and　zig-zag　theory　are　described　separately,　and　the　corresponding　advantage　and　disadvantage　are　presented　in　detail　with　the　fundamental　assumption　and　applicable　condition.　The　available　analytical　and　numerical　simulations　of　composite　structure　are　reviewed　to　predict　the　mechanical　property　and　analyze　the　bending,　buckling,　vibration,　and　multi-field　coupling　behaviors　via　finite　element　method,　meshless　method　or　multiscale　method.　The　recent　development　of　the　applications　of　composite　laminated　structures　are　summarized　in　damage　detection　and　vibration　control,　and　the　emphases　are　placed　on　modal　analysis,　energy　harvester　and　vibration　suppression.　The　current　challenge　and　future　work　of　composite　structures　are　explored　from　fundamental　research　and　potential　applications.