Modern research into carcinogenesis has undergone three phases. Surgeons and pathologists started the first phase and established autopsy and biopsy as routine pathology services, in turn establishing morphological traits for tumors and establishing immortality and autonomy as indispensable criteria for neoplasms. A century ago medical doctors and biologists initiated “experimental cancer research” as the second phase, in which they, with help from chemists, established many chemical-induced animal models of carcinogenesis. In this 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. For the last 40 years, 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 peers had already collected the lesions from animals for analyses of “cancer” mechanisms before the lesions became autonomous. We herein review 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 all 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.