The presentation proceeds along the following lines: a. it explains the dual role of education in social stratification of modern societies - main vehicle of intergenerational mobility as well as main vehicle of intergenerational status reproduction b. it explains trends and cross-national comparisons of inequality of education opportunity (IEO) c. it highlights the main features of education systems that are related to the amount of inequality of education opportunity (these are - for instance - the level of ability tracking, existence of centralized standardized exams, existence of tuition fees, special arrangement for adult learners, diversification of the system of higher education, etc.) d. it summarizes what current population trends might imply for trends in IEO; since some imply increasing inequality (everything else being equal), then e. I conclude - how could education systems be modified so that IEO does not increase as a result.