One of the fundamental challenges facing the cell is to accurately copy its genetic material to daughter cells. When this process goes awry, genomic instability ensues in which genetic alterations ranging from nucleotide changes to chromosomal translocations and aneuploidy occur. Organisms have developed multiple mechanisms that can be classified into two major classes to ensure the fidelity of DNA replication. The first class includes mechanisms that prevent premature initiation of DNA replication and ensure that the genome is fully replicated once and only once during each division cycle. These include cyclin-dependent kinase (CDK)-dependent mechanisms and CDK-independent mechanisms. Although CDK-dependent mechanisms are largely conserved in eukaryotes, higher eukaryotes have evolved additional mechanisms that seem to play a larger role in preventing aberrant DNA replication and genome instability. The second class ensures that cells are able to respond to various cues that continuously threaten the integrity of the genome by initiating DNA-damage-dependent "checkpoints" and coordinating DNA damage repair mechanisms. Defects in the ability to safeguard against aberrant DNA replication and to respond to DNA damage contribute to genomic instability and the development of human malignancy. In this article, we summarize our current knowledge of how genomic instability arises, with a particular emphasis on how the DNA replication process can give rise to such instability.