Cancer stem cells (CSCs) are subpopulations of multipotent stem cells (SCs) responsible for the initiation, long-term clonal maintenance, growth and spreading of most human neoplasms. Reportedly, CSCs share a very robust DNA damage response (DDR) with embryonic and adult SCs, which allows them to survive endogenous and exogenous genotoxins. A range of experimental evidence indicates that CSCs have high but heterogeneous levels of replication stress (RS), arising from, and being boosted by, endogenous causes, such as specific genetic backgrounds (e.g., p53 deficiency) and/or aberrant karyotypes (e.g., supernumerary chromosomes). A multipronged RS response (RSR) is put in place by CSCs to limit and ensure tolerability to RS. The characteristics of such dedicated cascade have two opposite consequences, both relevant for cancer therapy. On the one hand, RSR efficiency often increases the reliance of CSCs on specific DDR components. On the other hand, the functional redundancy of pathways of the RSR can paradoxically promote the acquisition of resistance to RS- and/or DNA damage-inducing agents. Here, we provide an overview of the molecular mechanisms of the RSR in cancer cells and CSCs, focusing on the role of CHK1 and some emerging players, such as PARP1 and components of the homologous recombination repair, whose targeting can represent a long-term effective anti-CSC strategy.