Climate models are used in a variety of applications: for the understanding of the interactions between different components of the climate system, for seasonal and decadal predictions, and for climate projections based on possible scenarios for future emissions. The current generation of climate models uses structured-mesh methods for the spatial discretization of both the atmosphere and the ocean. Typical biases with respect to observations may partly be connected to systematic errors arising from these traditional discretization methods. The goals of this thesis are (i) to develop a new global climate model with a multi-resolution sea ice-ocean component (FESOM) based on unstructured meshes coupled to an interactive atmospheric component (ECHAM6), (ii) a careful validation against observational data and other models, and (iii) the application of this new model to scientific questions for which the multi-resolution approach is particularly well suited. The multi-resolution approach allows to increase the spatial resolution locally in ocean regions of particular interest, e.g. at coastlines or near deep-water production sites, and to study the influence of small-scale processes on the global climate system and their interactions with the atmosphere. The first part of this thesis deals with the coupling of the existing models ECHAM6 and FESOM which was a fundamental task in the course of this dissertation. The physics of the turbulent exchange of moisture, momentum, and heat at the atmosphere-ocean interface is described in detail. Due to the different geometrical representation of the land-sea distribution in the models, the conservation of net fluxes between the models has to be guaranteed and one particular solution is given. As a next step, the mean climate state of a long control run with ECHAM6-FESOM forced with present-day (1990) greenhouse gas and aerosol concentrations is analyzed. The simulated mean climate compares favorably to observations—with typical biases known from other models at that resolution—and is even slightly better than the average over five well-established models according to objective performance indices. A similar result is found for the simulated variability, in particular atmospheric teleconnection patterns and spatio-temporal variability patterns in the ocean. An examination of strong cooling trends in global mean surface temperature in the present-day control run allows to attribute the observed ”hiatus period” to natural variability of the climate system that is able to temporarily mask the externally forced warming trend. The potential of unstructured-mesh methods for global climate modeling is illustrated via two simulations with ECHAM6-FESOM that differ only in the spatial resolution in the equatorial belt. An increased resolution in the ocean leads, inter alia, to a better simulation of the narrow equatorial current systems and a reduced cold bias in the western tropical Pacific. Connected to this are improvements in the simulation of the El Nino–Southern Oscillation phenomenon. Future setups with ECHAM6-FESOM will apply strongly increased resolution in other key areas of the ocean, e.g. in the Arctic or in the Gulfstream and North Atlantic current regions. These setups will allow to study the importance of different key regions in the global climate system as well as their role in causing typical systematic errors encountered in the current generation of climate models.