Mammalian chromosome duplication progresses in a precise order and is subject to constraints that are often relaxed in developmental disorders and malignancies. Molecular information about the regulation of DNA replication at the chromatin level is lacking because protein complexes that initiate replication seem to bind chromatin indiscriminately. High-throughput sequencing and mathematical modelling have yielded detailed genome-wide replication initiation maps. Combining these maps and models with functional genetic analyses suggests that distinct DNA-protein interactions at subgroups of replication initiation sites (replication origins) modulate the ubiquitous replication machinery and supports an emerging model that delineates how indiscriminate DNA-binding patterns translate into a consistent, organized replication programme.