The talk reviews two approaches to high-order variable-resolution modeling that have recently been designed for atmospheric weather and climate models. The first approach is based on the Adaptive Mesh Refinement (AMR) library Chombo that supports fourth-order finite volume methods for block-structured adaptive meshes on cubed-sphere grids. The Chombo-AMR model has been jointly developed by the Lawrence Berkeley National Laboratory and the University of Michigan. The second variable-resolution grid approach is based on the Spectral Element (SE) method that has been implemented on a cubed-sphere grid in the Community Atmosphere Model (CAM). The latter has been jointly developed by the National Center for Atmospheric Research (NCAR) and various Department of Energy laboratories.