Myc is a cellular oncogene frequently deregulated in cancer that has the ability to stimulate cellular growth by promoting a number of proliferative and pro-survival pathways. Here we will focus on how Myc controls a number of diverse cellular processes that converge to ensure processivity and robustness of DNA synthesis, thus preventing the inherent replicative stress responses usually evoked by oncogenic lesions. While these processes provide cancer cells with a long-term proliferative advantage, they also represent cancer liabilities that can be exploited to devise innovative therapeutic approaches to target Myc overexpressing tumors. This article is part of a Special Issue entitled: Myc proteins in cell biology and pathology.