Massimo Livi-Bacci's The Concise History of World Population talks about the "demographic transition" in modern societies, as all studies of population do. In pre-modern societies, most families had many children because quite a few of them would die before reaching adulthood. It was also common for women to die in childbirth, and the fathers to die before their children reached maturity. High fertility made sense in a world of high and uncertain mortality.
Modern societies made huge improvements in diet, sanitation, and, later in medicine. These improvements reduced deaths from infectious diseases, especially for children. As a result, the mortality rate at young ages went down, and life expectancy went up significantly. For a time, societies kept having lots of kids, but fewer of them died young. Thus, the population boomed. After a generation or so, culture caught up with the new facts of life, and people had fewer kids. The transition from high fertility/high mortality to low fertility/low mortality was complete.
All the rich societies made this transition a long time ago. Most poor societies are making this transition now. The massive population explosion of the 20th century is leveling off.
What interested me most about this familiar story was a second point that Livi-Bacci noted. Modern societies don't just live longer, they live more reliably. Modern societies have a more predictable life course. Not only is there a standard path (or several standard paths for different classes), but ordinary people were much more likely to actually live out that standard path.
The bedrock idea of Max Weber's sociology is that modern society has rationalized the world, has taken the disparate, organic, messy ways that people here and there did things and re-ordered them according to a rule. Weber famously connected the rationalization of religious life with the rationalization of economic life. Similar studies have been done about modern political rationalization, and rationalization in other cultural spheres, most notably in science.
What I saw in reading Livi-Bacci is that the modern world also rationalized the life course itself. When parents can expect their children to live, and can expect to live long enough themselves to see their grandchildren, their entire approach to life is changed. Hard work, savings, investment, planning, building up the rest of the social order all make more sense if most people can count on living out a rationalized life course.
And that is the greatest demographic transition of all.