Beginning with the earliest expeditions to the poles, over 100 years ago, scientists have compiled an impressive list of polar taxa whose body sizes are unusually large. This phenomenon has become known as 'polar gigantism'. In the intervening years, biologists have proposed a multitude of hypotheses to explain polar gigantism. These hypotheses run the gamut from invoking release from physical and physiological constraints, to systematic changes in developmental trajectories, to community-level outcomes of broader ecological and evolutionary processes. Here we review polar gigantism and emphasize two main problems. The first is to determine the true strength and generality of this pattern: how prevalent is polar gigantism across taxonomic units? Despite many published descriptions of polar giants, we still have a poor grasp of whether these species are unusual outliers or represent more systematic shifts in distributions of body size. Indeed, current data indicate that some groups show gigantism at the poles whereas others show nanism. The second problem is to identify underlying mechanisms or processes that could drive taxa, or even just allow them, to evolve especially large body size. The contenders are diverse and no clear winner has yet emerged. Distinguishing among the contenders will require better sampling of taxa in both temperate and polar waters and sustained efforts by comparative physiologists and evolutionary ecologists in a strongly comparative framework.