Transmissible tumours, while rare, present a fascinating opportunity to examine the evolutionary dynamics of cancer as both an infectious agent and an exotic, invasive species. Only three naturally-occurring transmissible cancers have been observed so far in the wild: Tasmanian devil facial tumour diseases, canine transmissible venereal tumour, and clam leukaemia. Here, we define four conditions that are necessary and sufficient for direct passage of cancer cells between either vertebrate or invertebrate hosts. Successful transmission requires environment and behaviours that facilitate transfer of tumour cells between hosts including: tumour tissue properties that promote shedding of large numbers of malignant cells, tumour cell plasticity that permits their survival during transmission and growth in a new host, and a 'permissible' host or host tissue. This rare confluence of multiple host- and tumour cell-traits both explains the rarity of tumour cell transmission and provides novel insights into the dynamics that both promote and constrain their growth.