In a lifetime, a human being synthesizes approximately 2×10¹⁶ meters of DNA, a distance that corresponds to 130,000 times the distance between the Earth and the Sun. This daunting task is executed by thousands of replication forks, which progress along the chromosomes and frequently stall when they encounter DNA lesions, unusual DNA structures, RNA polymerases, or tightly-bound protein complexes. To complete DNA synthesis before the onset of mitosis, eukaryotic cells have evolved complex mechanisms to process and restart arrested forks through the coordinated action of multiple nucleases, topoisomerases, and helicases. In this review, we discuss recent advances in understanding the role and regulation of nucleases acting at stalled forks with a focus on the nucleolytic degradation of nascent DNA, a process commonly referred to as fork resection. We also discuss the effects of deregulated fork resection on genomic instability and on the unscheduled activation of the interferon response under replication stress conditions.