Cenozoic climate change is marked by a deterioration of climate from the warm early Eocene, to cooler, drier, conditions as in the present glacial/interglacial cycles. The marine oxygen isotopic record indicates precipitous cooling at the Eocene-Oligocene boundary 33.5 Ma ago. This climatic step is also found in paleoprecipitation estimates from paleosols in Oregon and Montana, but is a small part of a long, steady decline across the Eocene-Oligocene boundary, rather than a sudden shift from one steady state to another. The large shift in the oxygen isotopic record probably represents the effect of ice accumulation in the initial glaciation and oceanic isolation of Antarctica, and is a threshold intrinsic to the ocean circulation system. Our continental records, in contrast, reveal temperature and rainfall decline over some ten million years. This suggests that climate was being driven by a gradual process, rather than an isolated perturbation. The coevolution of grasslands and grazers, oceanographic reorganization or the uplift of mountain ranges are suitable processes, while singular events such as bolide impacts are not.