The process of cellular transformation has been amply studied in vitro using immortalized cell lines. Immortalized cells never have the normal diploid karyotype, nevertheless, they cannot grow over one another in cell culture (contact inhibition), do not form colonies in soft agar (anchorage-dependent growth) and do not form tumors when injected into immunodeficient rodents. All these characteristics can be obtained with additional chromosome changes. Multiple genetic rearrangements, including whole chromosome and gene copy number gains and losses, chromosome translocations, gene mutations are necessary for establishing the malignant cell phenotype. Most of the experiments detecting transforming ability of genes overexpressed and/or mutated in tumors (oncogenes) were performed using mouse embryonic fibroblasts (MEFs), NIH3T3 mouse fibroblast cell line, human embryonic kidney 293 cell line (HEK293), and human mammary epithelial cell lines (mainly HMECs and MC-F10A). These cell lines have abnormal karyotypes and are prone to progress to malignantly transformed cells. This review is aimed at understanding the mechanisms of cell immortalization by different "immortalizing agents", oncogene-induced cell transformation of immortalized cells and moderate response of the advanced tumors to anticancer therapy in the light of tumor "oncogene and chromosome addiction", intra-/intertumor heterogeneity, and chromosome instability.