The carcinogenic process is multistep in terms of its etiology and multifactor in terms of its evolution. In this context, the temporal accumulation of multiple genetic changes during multistage carcinogenesis that can be mediated at least in part by genomic instability may represent crucial components of tumor cell evolution. Evidence is accumulating indicating a close link between genomic instability and cancer initiation and progression. Neoplastic cells typically possess numerous genomic lesions, which may include sequence alterations (point mutations, small deletions, and insertions) and/or gross structural abnormalities in one or more chromosomes (large-scale deletions, rearrangements, gene amplifications). Furthermore karyotypic alterations, including whole chromosome loss or gain, ploidy changes (aneuploidy and polyploidy) and a variety of chromosome aberrations are common in tumor cells. Genomic instability also involves mitotic defects associated with centrosome abnormalities. However, the question of whether abnormal centrosomes cause genomic instability or develop secondary to other changes has not been conclusively resolved. In this review, the recent studies investigating genomic instability and aneuploidy in human cancer, centrosome amplification and the role of centrosomal duplication in chromosomal mis-segregetion, and genes implicated in regulating chromosome segregation, centrosomal amplification and progression in cancer cells are discussed.