Eukaryotic DNA replication is a complex process. Replication starts at thousand origins that are activated at different times in S phase and terminates when converging replication forks meet. Potential origins are much more abundant than actually fire within a given S phase. The choice of replication origins and their time of activation is never exactly the same in any two cells. Individual origins show different efficiencies and different firing time probability distributions, conferring stochasticity to the DNA replication process. High-throughput microarray and sequencing techniques are providing increasingly huge datasets on the population-averaged spatiotemporal patterns of DNA replication in several organisms. On the other hand, single-molecule replication mapping techniques such as DNA combing provide unique information about cell-to-cell variability in DNA replication patterns. Mathematical modelling is required to fully comprehend the complexity of the chromosome replication process and to correctly interpret these data. Mathematical analysis and computer simulations have been recently used to model and interpret genome-wide replication data in the yeast Saccharomyces cerevisiae and Schizosaccharomyces pombe, in Xenopus egg extracts and in mammalian cells. These works reveal how stochasticity in origin usage confers robustness and reliability to the DNA replication process.