DNA replication, the process of duplication of a cell's genetic content, must be carried out with great precision every time the cell divides, so that genetic information is preserved. Control mechanisms must ensure that every base of the genome is replicated within the allocated time (S-phase) and only once per cell cycle, thereby safeguarding genomic integrity. In eukaryotes, replication starts from many points along the chromosome, termed origins of replication, and then proceeds continuously bidirectionally until an opposing moving fork is encountered. In contrast to bacteria, where a specific site on the genome serves as an origin in every cell division, in most eukaryotes origin selection appears highly stochastic: many potential origins exist, of which only a subset is selected to fire in any given cell, giving rise to an apparently random distribution of initiation events across the genome. Origin states change throughout the cell cycle, through the ordered formation and modification of origin-associated multisubunit protein complexes. State transitions are governed by fluctuations of cyclin-dependent kinase (CDK) activity and guards in these transitions ensure system memory. We present here DNA replication dynamics, emphasizing recent data from the fission yeast Schizosaccharomyces pombe, and discuss how robustness may be ensured in spite of (or even assisted by) system randomness.