Abstract: Main procedures of meshless methods are reviewed and discussed. The approximation of meshless methods，the selection of weight function，the variational form and the discrete equation，and the numerical implementation are described. The discontinuous approximations and the approach of boundary conditions，and the coupling meshless methods to finite elements are studied. Two examples which use the EFG method are presented. Based on the investigation on the recent advances of the methods，the future development tendency of meshless methods is discussed and outlined.

Key words: Galerkin method, Meshless methods, Weight function