We recently described a novel form of cell division termed neosis, which appears to be the mode of escape of cells from senescence and is involved in the neoplastic transformation and progression of tumors (Cancer Biol & Therap 2004;3:207–18). Neosis is a parasexual somatic reduction division and is characterized by (1) DNA damage-induced senescence/mitotic crisis and polyploidization, (2) followed by production of aneuploid daughter cells via nuclear budding, (3) asymmetric cytokinesis and cellularization conferring extended, but, limited mitotic life span to the offspring, and (4) is repeated several times during tumor growth. The immediate neotic progeny are termed the Raju cells, which seem to transiently display stem cell properties. The Raju cells immediately undergo symmetric mitotic division and become mature tumor cells. Exposure of tumor cells to genotoxic agents yields neosis-derived Raju cell progenies that are resistant to genotoxins, thus contributing to the recurrence of drug-resistant tumor growth. Similar events have been described in the literature under different names through several decades, but have been neglected due to the lack of appreciation of the significance of this process in cancer biology. Here we review and interpret the literature in the light of our observations and the recent advances in self-renewal in cancer. Neosis paradigm of self-renewal of cancer growth is consistent with the telomere attrition, aging and origin of cancer cells after reactivation of telomerase, and constitutes an alternative to the cancer stem cell hypothesis. We summarize the arguments favoring Raju cells and not cancer stem cells, as the source of self-renewal in cancer and present a comprehensive hypothesis of carcinogenesis, encompassing various aspects of cancer biology including senescence, tumor suppressor genes, oncogenes, cell cycle checkpoints, genomic instability, polyploidy and aneuploidy, natural selection, apoptosis, endoapoptosis, development of resistance to radiotherapy and chemotherapy leading tumor progression into malignancy.