We describe the basic tenets of the current concepts of cancer biology, and review the recent advances on the suppressor role of senescence in tumor growth and the breakdown of this barrier during the origin of tumor growth. Senescence phenotype can be induced by (1) telomere attrition-induced senescence at the end of the cellular mitotic life span (MLS*) and (2) also by replication history-independent, accelerated senescence due to inadvertent activation of oncogenes or by exposure of cells to genotoxins. Tumor suppressor genes p53/pRB/p16INK4A and related senescence checkpoints are involved in effecting the onset of senescence. However, senescence as a tumor suppressor mechanism is a leaky process and senescent cells with mutations or epimutations in these genes escape mitotic catastrophe-induced cell death by becoming polyploid cells. These polyploid giant cells, before they die, give rise to several cells with viable genomes via nuclear budding and asymmetric cytokinesis. This mode of cell division has been termed neosis and the immediate neotic offspring the Raju cells. The latter inherit genomic instability and transiently display stem cell properties in that they differentiate into tumor cells and display extended, but, limited MLS, at the end of which they enter senescent phase and can undergo secondary/tertiary neosis to produce the next generation of Raju cells. Neosis is repeated several times during tumor growth in a non-synchronized fashion, is the mode of origin of resistant tumor growth and contributes to tumor cell heterogeneity and continuity. The main event during neosis appears to be the production of mitotically viable daughter genome after epigenetic modulation from the non-viable polyploid genome of neosis mother cell (NMC). This leads to the growth of resistant tumor cells. Since during neosis, spindle checkpoint is not activated, this may give rise to aneuploidy. Thus, tumor cells also are destined to die due to senescence, but may escape senescence due to mutations or epimutations in the senescent checkpoint pathway. A historical review of neosis-like events is presented and implications of neosis in relation to the current dogmas of cancer biology are discussed. Genesis and repetitive re-genesis of Raju cells with transient "stemness" via neosis are of vital importance to the origin and continuous growth of tumors, a process that appears to be common to all types of tumors. We suggest that unlike current anti-mitotic therapy of cancers, anti-neotic therapy would not cause undesirable side effects. We propose a rational hypothesis for the origin and progression of tumors in which neosis plays a major role in the multistep carcinogenesis in different types of cancers. We define cancers as a single disease of uncontrolled neosis due to failure of senescent checkpoint controls.