In　this　paper,　the　history　of　the　Melnikov　theory　is　summarized.　In　1963,　the　classical　Melnikov　method　was　presented　by　Melnikov,　a　Russian　scientist.　Until　now,　the　Melnikov　theory　has　been　extended　and　developed.　The　development　of　the　Melnikov　method　is　divided　into　three　historical　periods.　The　extension　and　application　of　Melnikov　theory　are　respectively　summed　up　in　each　historical　period,　in　which　the　situation　of　study　and　main　domestic　and　abroad　results　in　this　research　field　are　enumerated.　The　relationships,　problems　and　deficiencies　are　pointed　out　for　a　variety　of　Melnikov　theories.　In　addition,　another　global　perturbation　method,　i.e.,　energy　phase　theory,　is　set　forth　in　order　to　compare　with　two　theories　which　are　normally　used　to　investigate　multi-pulse　chaotic　motion　in　the　high-dimensional　nonlinear　systems.　The　brief　history,　the　theory　and　the　research　achievements　and　engineering　applications　of　the　energy　phase　theory　are　elucidated.　The　origin　of　the　energy　phase　theory　and　its　inherent　relations　with　the　Melnikov　theory　are　illustrated.　The　subject　investigated　in　the　energy　phase　method　is　contrast　with　that　in　the　extended　Melnikov　method　to　find　the　difference　between　them.　Disadvantages　and　open　problems　are　indicated　for　both　the　energy　phase　method　and　the　extended　Melnikov　method.　Furthermore,　theoretical　frames　of　these　two　methods　are　stated　briefly.　The　multi-pulse　chaotic　dynamics　for　a　rectangular　thin　plate,　simply　supported　at　the　fore-edge,　is　analyzed　by　using　both　of　them.　Numerical　simulation　further　verifies　the　analytical　prediction.　Finally,　deficiencies　of　these　two　theories　are　described　in　detail.　The　future　development　direction　of　the　global　perturbation　theory　is　demonstrated　too.