The initiation reactions of DNA synthesis are central processes during human chromosomal DNA replication. They are separated into two main processes: the initiation events at replication origins, the start of the leading strand synthesis for each replicon, and the numerous initiation events taking place during lagging strand DNA synthesis. In addition, a third mechanism is the re-initiation of DNA synthesis after replication fork stalling, which takes place when DNA lesions hinder the progression of DNA synthesis. The initiation of leading strand synthesis at replication origins is regulated at multiple levels, from the origin recognition to the assembly and activation of replicative helicase, the Cdc45-MCM2-7-GINS (CMG) complex. In addition, the multiple interactions of the CMG complex with the eukaryotic replicative DNA polymerases, DNA polymerase α-primase, DNA polymerase δ and ε, at replication forks play pivotal roles in the mechanism of the initiation reactions of leading and lagging strand DNA synthesis. These interactions are also important for the initiation of signalling at unperturbed and stalled replication forks, "replication stress" events, via ATR (ATM-Rad 3-related protein kinase). These processes are essential for the accurate transfer of the cells' genetic information to their daughters. Thus, failures and dysfunctions in these processes give rise to genome instability causing genetic diseases, including cancer. In their influential review "Hallmarks of Cancer: New Dimensions", Hanahan and Weinberg (2022) therefore call genome instability a fundamental function in the development process of cancer cells. In recent years, the understanding of the initiation processes and mechanisms of human DNA replication has made substantial progress at all levels, which will be discussed in the review.