We're quickly moving from the population explosion problem to the population implosion problem. No one planned it or made it happen. But, it looks like we're not actually going to overflow the planet with people standing shoulder to shoulder. Instead, the problem we're facing moving forward is a combination of longer lifespans and less children shifting the elderly support structure from a pyramid to a column.
A big driver of this is people moving up in job prospects around the world. Clearly in rich nations like the US, Japan and UK couples are working more and putting off having kids. But, also in the poorer nations people are moving to the cities because that's where the jobs are. Once there, the combination of high rent and great reductions in child mortality means it doesn't make sense any more to have lots of kids hoping that a few survive long enough to work at a young age. Instead of having babies rapidly, women around the world are going to work to bring in that second income needed to pay the bills in the city.
It's great news, really. It's just really scary really great news because we don't know how to set up a society where there aren't enough young people to support the elderly.