Element-Free　Galerkin　Method　(EFG)　is　a　typical　meshless　method.　Compared　with　other　meshless　methods,　EFG　method　has　simple,　definite　form,　and　can　achieve　highly　accurate　solution.　There　are　also　several　notable　advantages　in　the　applications　of　EFG　method,　such　as　only　required　discrete　nodal　data,　higher　order　continuity　of　the　solutions,　being　able　to　represent　high-gradient　stress　field　and　to　track　the　spread　process　of　crack　propagation.　At　present,　EFG　method　has　become　a　study　issue　in　computational　mechanics　field.　This　paper　is　concerned　with　the　EFG　method.　Some　major　problems　in　EFG,　such　as　choosing　base　function,　determining　radius　of　domain　of　influence,　introducing　essential　boundary　conditions,　are　addressed.　Meanwhile,　many　results　of　applications　of　EFG　are　introduced.　Finally,　the　prospect　of　EFG＇s　development　is　discussed.