The articles in this special issue show the vitality and progress of research on multigenerational aspects of social mobility, stratification, and inequality. The effects of the characteristics and behavior of grandparents and other kin on the statuses, resources, and positions of their descendants are best viewed in a demographic context. Intergenerational effects work through both the intergenerational associations of socioeconomic characteristics and also differential fertility and mortality. A combined socioeconomic and demographic framework informs a research agenda which addresses the following issues: how generational effects combine with variation in age, period, and cohort within each generation; distinguishing causal relationships across generations from statistical associations; how multigenerational effects vary across socioeconomic hierarchies, including the possibility of stronger effects at the extreme top and bottom; distinguishing between endowments and investments in intergenerational effects; multigenerational effects on associated demographic behaviors and outcomes (especially fertility and mortality); optimal tradeoffs among diverse types of data on multigenerational processes; and the variability across time and place in how kin, education, and other institutions affect stratification.