DNA replication stress is a constant threat that cells must manage to proliferate and maintain genome integrity. DNA replication stress responses, a subset of the broader DNA damage response (DDR), operate when the DNA replication machinery (replisome) is blocked or replication forks collapse during S phase. There are many sources of replication stress, such as DNA lesions caused by endogenous and exogenous agents including commonly used cancer therapeutics, and difficult-to-replicate DNA sequences comprising fragile sites, G-quadraplex DNA, hairpins at trinucleotide repeats, and telomeres. Replication stress is also a consequence of conflicts between opposing transcription and replication, and oncogenic stress which dysregulates replication origin firing and fork progression. Cells initially respond to replication stress by protecting blocked replisomes, but if the offending problem (e.g., DNA damage) is not bypassed or resolved in a timely manner, forks may be cleaved by nucleases, inducing a DNA double-strand break (DSB) and providing a means to accurately restart stalled forks via homologous recombination. However, DSBs pose their own risks to genome stability if left unrepaired or misrepaired. Here we focus on replication stress response systems, comprising DDR signaling, fork protection, and fork processing by nucleases that promote fork repair and restart. Replication stress nucleases include MUS81, EEPD1, Metnase, CtIP, MRE11, EXO1, DNA2-BLM, SLX1-SLX4, XPF-ERCC1-SLX4, Artemis, XPG, and FEN1. Replication stress factors are important in cancer etiology as suppressors of genome instability associated with oncogenic mutations, and as potential cancer therapy targets to enhance the efficacy of chemo- and radiotherapeutics.