Partial different equations with discontinuous coefficients having complex interface geometry are of great interests in practical applications. The design of body-fitted high-order finite element methods requires the construction of shape regular body-fitted meshes for complex geometry and also nonlinear element transforms from the reference element to the elements with curved boundary. In practical applications, it may be challenging to satisfy the conditions imposed on the nonlinear element transforms in the literature which depend on the geometry of the interface. In this talk we study high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems, which release the work of body-fitted mesh generation and provide a natural way to design high-order methods without resorting to nonlinear element transforms. We introduce new concepts of large element and interface deviation to solve the small cut cell problem of unfitted finite element methods. We construct a reliable algorithm to merge small interface elements with their surrounding elements to automatically generate the finite element mesh whose elements are large with respect to both domains. We show novel $hp$-domain inverse estimates which allow us to prove the stability of the finite element method under practical interface resolving mesh conditions and prove $hp$ a priori and a posteriori error estimates. We propose new basis functions for the interface elements to control the growth of the condition number of the stiffness matrix in terms of the finite element approximation order, the number of elements of the mesh, and the interface deviation. Numerical examples are presented to illustrate the competitive performance of the method. This talk is based on joint works with Ke Li, Yong Liu and Xueshuang Xiang.