Unstructured-mesh models are common in coastal ocean modeling, but their applications are still at the beginning stage in large-scale ocean and climate studies. Global ocean general circulation models formulated on unstructured meshes have matured during the last few years. Due to the flexibility in seamlessly varying grid resolution, using multi-resolution in a global configuration can be easily realized with such models. In these models, relatively low resolution remains in regions which are dynamically less important or less relevant for intended studies, so computational cost can be reduced. In this presentation, I will review the potential of unstructured-mesh modeling in large-scale ocean and climate applications, illustrate the advantages of the new generation models, and discuss considerations that should be taken when using them. Specifically, the Finite Element/volumE Sea-ice Ocean Model (FESOM) will be presented as an example. It is the first mature multi-resolution global ocean model of its kind, which is developed by the Alfred Wegener Institute Helmholtz Center for Polar and Marine Research (AWI). Results from the AWI Climate Model (AWI-CM) will also be presented to show the status of applying multi-resolution in climate modeling, including CMIP6 simulations. The recent model development will support the concept of improving model simulations while keeping computational cost, thus energy consumption, as low as possible.