This research line in quantitative historical sociology is situated at the interface of sociology and social history. It investigates differences in openness between societies, the size of such differences, and whether there has been a trend towards more social mobility in some or all parts of the world. If so, what are the driving forces behind this development? Following modernisation theory, it is argued that there is a trend away from traditional societies, where a person’s social position was essentially inherited, to more open ones, where social position depends upon individual achievement. Modernisation theory is tested against its rivals – notably status maintenance theory – using large data sets for numerous European countries and time periods (18th, 19th, and 20th centuries), mainly consisting of information from marriage registers.