In this talk, we will discuss our recent work for solving Maxwell interface problems on Unfitted Meshes. Maxwell interface problems are very senstive to the conformity of the approximation spaces, which poses challenges on unfitted mesh finite element methods, as most of them resort to non-conforming spaces. In this talk, we will begin with the H(curl) 2D virtual element method (VEM) and take its advantages of conformity on any polygonal shaped meshes. We will address its application to Maxwell equations on anisotropic meshes, which is applicable to background unfitted meshes cut by the interface. For the 3D case, we then present an immersed virtual element method (IVEM) by combining the conformity of VEM and robust approximation capabilities of immersed finite element methods (IFEM). The central idea is to develop local interface problems on interface elements and project their solutions to IFE spaces for computation. We will address the development of spaces including the well-posedness and computability, the scheme and the fast solver.