Genomically instable cancers are characterized by progressive loss and gain of chromosomal fragments, and the acquisition of complex genomic rearrangements. Such cancers, including triple-negative breast cancers and high-grade serous ovarian cancers, typically show aggressive behavior and lack actionable driver oncogenes. Increasingly, oncogene-induced replication stress or defective replication fork maintenance is considered an important driver of genomic instability. Paradoxically, while replication stress causes chromosomal instability and thereby promotes cancer development, it intrinsically poses a threat to cellular viability. Apparently, tumor cells harboring high levels of replication stress have evolved ways to cope with replication stress. As a consequence, therapeutic targeting of such compensatory mechanisms is likely to preferentially target cancers with high levels of replication stress and may prove useful in potentiating chemotherapeutic approaches that exert their effects by interfering with DNA replication. Here, we discuss how replication stress drives chromosomal instability, and the cell cycle-regulated mechanisms that cancer cells employ to deal with replication stress. Importantly, we discuss how mechanisms involving DNA structure-specific resolvases, cell cycle checkpoint kinases and mitotic processing of replication intermediates offer possibilities in developing treatments for difficult-to-treat genomically instable cancers.