Evidence for immortality and autonomy in animal cancer models is often not provided, which causes confusion on key issues of cancer biology.

Modern research into carcinogenesis has undergone three phases. Surgeons and pathologists started the first phase roughly 250 years ago, establishing morphological traits of tumors for pathologic diagnosis, and setting immortality and autonomy as indispensable criteria for neoplasms. A century ago, medical doctors, biologists and chemists started to enhance "experimental cancer research" by establishing many animal models of chemical-induced carcinogenesis for studies of cellular mechanisms. In this second phase, the two-hit theory and stepwise carcinogenesis of "initiation-promotion" or "initiation-promotion-progression" were established, with an illustrious finding that outgrowths induced in animals depend on the inducers, and thus are not authentically neoplastic, until late stages. The last 40 years are the third incarnation, molecular biologists have gradually dominated the carcinogenesis research fraternity and have established numerous genetically-modified animal models of carcinogenesis. However, evidence has not been provided for immortality and autonomy of the lesions from most of these models. Probably, many lesions had already been collected from animals for analyses of molecular mechanisms of "cancer" before the lesions became autonomous. We herein review the monumental work of many predecessors to reinforce that evidence for immortality and autonomy is essential for confirming a neoplastic nature. We extrapolate that immortality and autonomy are established early during sporadic human carcinogenesis, unlike the late establishment in most animal models. It is imperative to resume many forerunners' work by determining the genetic bases for initiation, promotion and progression, the genetic bases for immortality and autonomy, and which animal models are, in fact, good for identifying such genetic bases.