The population structure of Atlantic cod Gadus morhua L. in the Barents Sea and in fjords and coastal waters in Norway and northwestern Russia has been a controversial subject since the 1930s. Eight decades of scientific inquiry have compared migratory NE Arctic (NA) and stationary Norwegian and Russian coastal cod (NC). At one extreme the existence of 2 non-interbreeding groups is advocated, whereas others find support for low genetic differentiation due to substantial gene flow, with geographical distance being the limiting factor. We review studies of a wide range of phenotypic (e.g. growth, maturation, counts of vertebrae) and polymorphic genetic markers (e.g. allozymes, mtDNA, microsatellites, single nucleotide polymorphisms). Regardless of whether or not the observed differences have a genetic basis, 70% of the 54 reviewed papers conclude that NA and NC differ with respect to the characters studied. However, few papers remain after exclusion of those relying on characteristics or markers that are generally agreed to be subject to selection and therefore less suited to assessing population connectivity. The lack of studies examining the potential influence of environments on growth of annual zones in otoliths is surprising, since otoliths are used to categorize specimens in managing the NA and NC and in scientific papers. We conclude that it is still an open question whether NA and NC effectively make up 1 large population or >1 non-interbreeding 'groups'. As next-generation sequencing technology transforms 'population genetics' into 'population genomics', we will move towards a better understanding of differentiation among fish populations.