The recommendation that the Anthropocene be denoted as a geological epoch was recently rejected by the International Union of Geological Sciences. Here, we compare the scientific rationales presented for the Anthropocene, the Holocene and the six other epochs in the Cenozoic Era: the Pleistocene, the Pliocene, the Miocene, the Oligocene, the Eocene and the Paleocene. We also present a historical perspective on the process through which the Holocene was accepted as a formal geological epoch. We conclude that, from a purely geological perspective, the scientific case for the Anthropocene as a geological epoch is stronger than the case for the Holocene and as good as or better than the cases for several other epochs in the Cenozoic Era.