Genome stability is key for healthy cells in healthy organisms, and deregulated maintenance of genome integrity is a hallmark of aging and of age-associated diseases including cancer and neurodegeneration. To maintain a stable genome, genome surveillance and repair pathways are closely intertwined with cell cycle regulation and with DNA transactions that occur during transcription and DNA replication. Coordination of these processes across different time and length scales involves dynamic changes of chromatin topology, clustering of fragile genomic regions and repair factors into nuclear repair centers, mobilization of the nuclear cytoskeleton, and activation of cell cycle checkpoints. Here, we provide a general overview of cell cycle regulation and of the processes involved in genome duplication in human cells, followed by an introduction to replication stress and to the cellular responses elicited by perturbed DNA synthesis. We discuss fragile genomic regions that experience high levels of replication stress, with a particular focus on telomere fragility caused by replication stress at the ends of linear chromosomes. Using alternative lengthening of telomeres (ALT) in cancer cells and ALT-associated PML bodies (APBs) as examples of replication stress-associated clustered DNA damage, we discuss compartmentalization of DNA repair reactions and the role of protein properties implicated in phase separation. Finally, we highlight emerging connections between DNA repair and mechanobiology and discuss how biomolecular condensates, components of the nuclear cytoskeleton, and interfaces between membrane-bound organelles and membraneless macromolecular condensates may cooperate to coordinate genome maintenance in space and time.