Structure-specific endonucleases (SSEs) have key roles in DNA replication, recombination and repair, and emerging roles in transcription. These enzymes have specificity for DNA secondary structure rather than for sequence, and therefore their activity must be precisely controlled to ensure genome stability. In this Review, we discuss how SSEs are controlled as part of genome maintenance pathways in eukaryotes, with an emphasis on the elaborate mechanisms that regulate the members of the major SSE families - including the xeroderma pigmentosum group F-complementing protein (XPF) and MMS and UV-sensitive protein 81 (MUS81)-dependent nucleases, and the flap endonuclease 1 (FEN1), XPG and XPG-like endonuclease 1 (GEN1) enzymes - during processes such as DNA adduct repair, Holliday junction processing and replication stress. We also discuss newly characterized connections between SSEs and other classes of DNA-remodelling enzymes and cell cycle control machineries, which reveal the importance of SSE scaffolds such as the synthetic lethal of unknown function 4 (SLX4) tumour suppressor for the maintenance of genome stability.