Abstract: The development of an extended finite element method (XFEM) is investigated and the relation between XFEM and some other numerical methods is illustrated. First, the backgrounds and the development of meshfree methods are surveyed. Comparative analysis of them is given from the phase of approximation construction. Based on the general form of partition of unity, the characteristics of XFEM and the relations with conventional FE and other meshfree methods are presented. The main research domain about the applications and theory foundation of XFEM are summarized. And the prospect of XFEM is evaluated.