In this lecture I will consider the principles of Bayesian modelling for building archaeological chronologies. Stratigraphic and other prior information can be used to constrain the results of radiocarbon dating by using a mathematical model. This approach also allows us to infer probability distributions for events which cannot be dated directly, for example, the founding of a site. I will illustrate the principles using application to radiocarbon dating the Anglo-Saxon Church at Brixworth, England, and ESR dating of the hominid fossils from Border Cave, South Africa. The internal chronology of the Trypillia mega-site at Nebelivka, Ukraine, offers a particular challenge to chronology construction because there are few stratigraphic relationships between structures. However, there are many hypotheses about the relationship between spatial structure and the development of the site. If these hypotheses are treated alternative sets of prior information, the statistical method of model choice can be used to test the hypotheses against the radiocarbon data.