Many conventional chemotherapies used in cancer treatment exert their effect by inflicting DNA damage. Highly proliferative tissues, as well as tumour cells, are particularly vulnerable to this damage resulting in unwanted toxicities. In contrast, a targeted therapeutic approach has the aim of specifically eliminating cancer cells but with a reduced effect on healthy tissue. New therapies have been developed that target the replication stress response (RSR), a branch of the broader DNA damage response that specifically deals with interferences of the normal DNA replication program. Different pharmaceutical companies have developed inhibitors of the RSR kinases ATR, CHK1 and WEE1, which are currently at different phases of clinical development. Here, we review how the RSR works at the molecular level, what is the rationale for its targeting, and how we envisage its best use in the clinic, based on patient selection and combination therapies supported by in vitro and in vivo preclinical studies.