Fifty years ago, when Baby Boomers were starting families, demographers looked at the statistics and started to panic. World population was growing exponentially, meaning that eventually there would be more people than the world could sustain, and it would happen fast. But, like what happened in China, statistics and extrapolations don't tell the entire story. The exponential growth chart went awry, and population growth slowed. It hasn't gone down globally, but it isn't growing the way it used to. There are many reasons for that, as MinuteEarth explains.
However, fertility rate and population density varies widely by location, and so do demographics. Some countries are already lopsided, with more older people than young people, while other places have plenty of children. While we shouldn't worry about a population explosion, there are challenges in places that go to the extreme in any of those parameters.