Although every organism shares some common features of replication, this process varies greatly among eukaryotic species. Current data show that mathematical models of the organization of origins based on possibility theory may be applied (and remain accurate) in every model organism i.e. from yeast to humans. The major differences lie within the dynamics of origin firing and the regulation mechanisms that have evolved to meet new challenges throughout the evolution of the organism. This article elaborates on the relations between chromatin structure, organization of origins, their firing times and the impact that these features can have on genome stability, showing both differences and parallels inside the eukaryotic domain.