Accurate DNA replication is essential for the maintenance of genome stability and the generation of healthy offspring. When DNA replication is challenged, signals accumulate at blocked replication forks that elicit a multifaceted cellular response, orchestrating DNA replication, DNA repair and cell cycle progression. This replication stress response promotes the recovery of DNA replication, maintaining chromosome integrity and preventing mutations. Defects in this response are linked to heightened genetic instability, which contributes to tumorigenesis and genetic disorders. Iron–sulfur (Fe-S) clusters are emerging as important cofactors in supporting the response to replication stress. These clusters are assembled and delivered to target proteins that function in the cytosol and nucleus via the conserved cytosolic Fe-S cluster assembly (CIA) machinery and the CIA targeting complex. This review summarizes recent advances in understanding the structure and function of the CIA machinery in yeast and mammals, emphasizing the critical role of Fe-S clusters in the replication stress response.