DNA replication is a tightly controlled process that ensures the faithful duplication of the genome. However, DNA damage arising from both endogenous and exogenous assaults gives rise to DNA replication stress associated with replication fork slowing or stalling. Therefore, protecting the stressed fork while prompting its recovery to complete DNA replication is critical for safeguarding genomic integrity and cell survival. Specifically, the plasticity of the replication fork in engaging distinct DNA damage tolerance mechanisms, including fork reversal, repriming, and translesion DNA synthesis, enables cells to overcome a variety of replication obstacles. Furthermore, stretches of single-stranded DNA generated upon fork stalling trigger the activation of the ATR kinase, which coordinates the cellular responses to replication stress by stabilizing the replication fork, promoting DNA repair, and controlling cell cycle and replication origin firing. Deregulation of the ATR checkpoint and aberrant levels of chronic replication stress is a common characteristic of cancer and a point of vulnerability being exploited in cancer therapy. Here, we discuss the various adaptive responses of a replication fork to replication stress and the roles of ATR signaling that bring fork stabilization mechanisms together. We also review how this knowledge is being harnessed for the development of checkpoint inhibitors to trigger the replication catastrophe of cancer cells.