The complexity of the state-of-the-art Ocean General Circulation Models (OGCMs) has increased and the quality of the model systems has improved considerably over the last decades. The improvement is caused by a variety of factors ranging from improved representation of key physical and dynamical processes, parallel development of at least three classes of OGCM systems, accurate and cost-effective numerical schemes, an unprecedented increase in computational resources, and the availability of synoptic, multidecadal atmospheric forcing fields. The implications of these improvements are that the present generation of OGCMs can, for the first time, complement available ocean observations and be used to guide forthcoming ocean observation strategies. OGCMs are also extensively used as laboratories for assessing cause-relationships for observed changes in the marine climate system, and to assess how the ocean system may change in response to, for instance, anomalous air-sea fluxes of heat, freshwater, and momentum. The Nordic Seas are a particularly challenging region for OGCMs because of characteristic length scales of only a few to about 10 km, a variety of complex and interrelated ocean processes, and extreme air-sea fluxes. This paper gives an overview of the status of the prognostic modelling of the Nordic Seas marine climate system. To exemplify the status, we present output from two widely different state-of-the-art OGCM systems. We also address processes that are still inadequately described in the current generation of OGCMs, thus providing guidelines for the future development of model systems particularly tailored for the Nordic Seas region.