Abstract: Many problems in physics, engineering, and other fields involve a certain level of coupling between different physical systems. For many multi-physics problems, the most difficult part is dealing with an interface, which separates two phases of matter; each may be solid, liquid, or gaseous. The extended finite element method (XFEM), which extends the classical FEM by enriching the numerical solution space locally around the interface with discontinuous functions, has shown its potential in a variety of applications that involve non-smooth solutions near interface. In this talk, we will discuss XFEM with DG schemes to solve elliptic interface problems. We show the optimal convergence rate for any order XFE space if the solution satisfies curtain regularity in each subdomain. The talk is based on the joint research works with Jinchao Xu, Yuanming Xiao, and Shuo Zhang.