Unstructured meshes offer geometric flexibility. In the context of large-scale ocean modeling they enable simulations with a regional focus in an otherwise global setup, without nesting or open boundaries. We follow this concept by developing and exploiting FESOM, the Finite-Element Sea ice-Ocean circulation Model. A brief review of current FESOM-assisted research will be given, to illustrate what is possible to achieve in the framework of this concept. In particular, we present results from studies of freshwater transport through the Canadian Arctic Archipelago, simulations of the impact of Greenland ice sheet melting on the sea level, results from the high-resolution (about 9 km) Arctic runs, as well as results related to the dense water formation around Antarctica. In most case we are dealing with coarse global setups (around 1 degree), refined to 3 - 20 km in the area of interest. FESOM is now coupled to ECHAM5 and ECHAM6 atmospheric models and is also used in climate studies, with the same basic concept of focus on regional dynamics. There are numerous challenges both on computational and numerical sides which have to be solved to ensure wider acceptance of unstructured meshes by the oceanographic community. First, the numerical efficiency of unstructured-mesh models has to be essentially improved, which includes data storage, solvers, domain decomposition, load balance and other related issues. Second, we see the need for more accurate (less dissipative) numerical transport algorithms. FESOM is based on the stabilized P1-P1 discretization. We are exploring two closely related finite-volume discretizations (vertex-vertex and cell-vertex) which promise higher numerical efficiency. A brief review of related efforts will be given.