Well-nourished cells in a favorable environment (well supplied with growth factors, cytokines, and/or hormones and free from stresses, ionizing radiation, etc.) will grow, replicate their genome, and divide into two daughter cells, fully prepared to repeat the process. This cycle of DNA replication and division underlies all aspects of biological growth, reproduction, repair and development. As such, it is essential that the cell's genome be guarded against damage during the replication/division process, lest the error(s) be irrevocably passed down to all future generations of progeny. Hence, cell cycle progression is closely guarded against major sources of errors, in particular DNA damage and misalignment of replicated chromosomes on the mitotic spindle. In this review article we examine closely the molecular mechanisms that maintain genomic integrity during the cell division cycle, and we find an unexpected and intriguing arrangement of concatenated and nested bistable toggle switches. The topology of the network seems to play crucial roles in maintaining the stability of the genome during cell proliferation.