There are pockets where population has, by and large, peaked and is predicted to decline over the next 40 years, Europe being one such.  The rest of the planet is still pumping out the kids.  

Not only Europe: many non-European countries have pretty much stopped "pumping out the kids". If you look at projected population growth and total fertility rates, you can see that even today, many populous countries are well below the replacement rate: China, Russia, Japan, but also Brazil, Iran, and even Venezuela and Mexico considering that in "poor" countries, the replacement rate is higher than 2.1 children per woman.

Today, the bulk of the population growth is in sub-Saharan Africa (but many African countries -except Nigeria and Congo - are starting from a rather low population) and especially the Indian sub-continent: India is expected to overtake China as the most populous country before 2030.

Even if the world population is expected to stop growing and even start decreasing before the end of this century, this doesn't mean there's not going to be a considerable strain on resources before that: especially in South Asia: India, Pakistan, Bangladesh, Indonesia, the Philippines and even Afghanistan. This, combined with female infanticide and selective abortion, is not boding well for the future of the region.