This paper re-evaluates whether we are really at the start of a mass extinction caused by humans. I consider the present, past and future of human-caused extinctions. As regards the present, estimates of extinction rates based on Red Data Books underestimate real values by a large factor, because the books evaluate only those species that have attracted specific attention and searches. Especially in tropical areas with few resident biologists, many poorly known species go extinct without having been the object of specific attention, and others disappear even before being described. A 'green list' of species known to be secure is needed to complement 'red books' of species known to be extinct. As regards the past, it is now clear that the first arrival of humans at any oceanic island with no previous human inhabitants has always precipitated a mass extinction in the island biota. Well-known victims include New Zealand's moas, Madagascar's giant lemurs, and scores of bird species on Hawaii and other tropical Pacific islands. Late-Pleistocene or Holocene extinctions of large mammals after the first arrival of humans in North America, South America and Australia may also have been caused by humans. Hence human-caused mass extinction is not a hypothesis for the future but an event that has been underway for thousands of years. As regards the future, consideration of the main mechanisms of human-caused extinctions (overhunting, effects of introduced species, habitat destruction, and secondary ripple effects) indicates that the rate of extinction is accelerating. The basic reason is that there are now more humans than ever before, armed with more potent destructive technology, and encroaching on the world's most species-rich habitats: the continental tropical rainforests.