In their influential reviews, Hanahan and Weinberg coined the term ‘Hallmarks of Cancer’ and described genome instability as a property of cells enabling cancer development. Accurate DNA replication of genomes is central to diminishing genome instability. Here, the understanding of the initiation of DNA synthesis in origins of DNA replication to start leading strand synthesis and the initiation of Okazaki fragment on the lagging strand are crucial to control genome instability. Recent findings have provided new insights into the mechanism of the remodelling of the prime initiation enzyme, DNA polymerase α-primase (Pol-prim), during primer synthesis, how the enzyme complex achieves lagging strand synthesis, and how it is linked to replication forks to achieve optimal initiation of Okazaki fragments. Moreover, the central roles of RNA primer synthesis by Pol-prim in multiple genome stability pathways such as replication fork restart and protection of DNA against degradation by exonucleases during double-strand break repair are discussed.