The replication-timing program constitutes a key element of the organization and coordination of numerous nuclear processes in eukaryotes. This program is established at a crucial moment in the cell cycle and occurs simultaneously with the organization of the genome, thus indicating the vital significance of this process. With recent technological achievements of high-throughput approaches, a very strong link has been confirmed between replication timing, transcriptional activity, the epigenetic and mutational landscape, and the 3D organization of the genome. There is also a clear relationship between replication stress, replication timing, and genomic instability, but the extent to which they are mutually linked to each other is unclear. Recent evidence has shown that replication timing is affected in cancer cells, although the cause and consequence of this effect remain unknown. However, in-depth studies remain to be performed to characterize the molecular mechanisms of replication-timing regulation and clearly identify different cis- and trans-acting factors. The results of these studies will potentially facilitate the discovery of new therapeutic pathways, particularly for personalized medicine, or new biomarkers. This review focuses on the complex relationship between replication timing, replication stress, and genomic instability.