Human cancers share properties referred to as hallmarks, among which sustained proliferation, escape from apoptosis, and genomic instability are the most pervasive. The sustained proliferation hallmark can be explained by mutations in oncogenes and tumor suppressors that regulate cell growth, whereas the escape from apoptosis hallmark can be explained by mutations in the TP53, ATM, or MDM2 genes. A model to explain the presence of the three hallmarks listed above, as well as the patterns of genomic instability observed in human cancers, proposes that the genes driving cell proliferation induce DNA replication stress, which, in turn, generates genomic instability and selects for escape from apoptosis. Here, we review the data that support this model, as well as the mechanisms by which oncogenes induce replication stress. Further, we argue that DNA replication stress should be considered as a hallmark of cancer because it likely drives cancer development and is very prevalent.