A contagious tumour threatens to wipe out the famous Tasmanian devil, a ferocious marsupial animal. Could contagious cancers arise in humans, too? Given that humans have great genetic diversity and can avoid behaving in ways that would foster tumour transmission, it might seem safe to assume that our species can readily avoid the fate of the Tasmanian devil. Indeed, if a person were bitten by an infected Tasmanian devil or by a dog with the canine transmissible tumour, the person’s genetic makeup, being so different from that of the animals, would probably ensure a strong immune response able to detect and kill the invading cells. Thus, the bitten individual would not get sick or start spreading the disease to others. There are grounds for concern, though. Contagious cancers could, in theory, arise in a group of great apes with low genetic diversity because of population declines. If they were hunted by human populations with many members having impaired immunity, the close contact might enable tumour cells to transfer to humans and then spread. Such conditions exist where humans with a high HIV prevalence hunt endangered apes. Although this scenario is possible, we suspect that cross-species transmission is not the most likely way that a contagious cancer would arise in humans. We hold this view in part because no known cases of cross-species transmission of the dog cancer have occurred in nature, although the disease has been experimentally transferred to related canines in the laboratory.