It is thought that the Northern Hemisphere experienced only ephemeral glaciations from the Late Eocene to the Early Pliocene epochs (about 38 to 4 million years ago), and that the onset of extensive glaciations did not occur until about 3 million years ago. Several hypotheses have been proposed to explain this increase in Northern Hemisphere glaciation during the Late Pliocene. Here we use a fully coupled atmosphere-ocean general circulation model and an ice-sheet model to assess the impact of the proposed driving mechanisms for glaciation and the influence of orbital variations on the development of the Greenland ice sheet in particular. We find that Greenland glaciation is mainly controlled by a decrease in atmospheric carbon dioxide during the Late Pliocene. By contrast, our model results suggest that climatic shifts associated with the tectonically driven closure of the Panama seaway, with the termination of a permanent El Niño state or with tectonic uplift are not large enough to contribute significantly to the growth of the Greenland ice sheet; moreover, we find that none of these processes acted as a priming mechanism for glacial inception triggered by variations in the Earth's orbit.