The world's population could decline

Not a decrease in the rate of increase (which has already happened), but an actual decline in numbers:

[t]he rate of global population growth has slowed. And it’s expected to keep slowing. Indeed, according to experts’ best estimates, the total population of Earth will stop growing within the lifespan of people alive today.

And then it will fall.

This is a counterintuitive notion in the United States, where we’ve heard often and loudly that world population growth is a perilous and perhaps unavoidable threat to our future as a species. But population decline is a very familiar concept in the rest of the developed world, where fertility has long since fallen far below the 2.1 live births per woman required to maintain population equilibrium...

American media have largely ignored the issue of population decline for the simple reason that it hasn’t happened here yet. Unlike Europe, the United States has long been the beneficiary of robust immigration. This has helped us not only by directly bolstering the number of people calling the United States home but also by propping up the birthrate, since immigrant women tend to produce far more children than the native-born do...

Moreover, the poor, highly fertile countries that once churned out immigrants by the boatload are now experiencing birthrate declines of their own. From 1960 to 2009, Mexico’s fertility rate tumbled from 7.3 live births per woman to 2.4, India’s dropped from six to 2.5, and Brazil’s fell from 6.15 to 1.9. Even in sub-Saharan Africa, where the average birthrate remains a relatively blistering 4.66, fertility is projected to fall below replacement level by the 2070s. This change in developing countries will affect not only the U.S. population, of course, but eventually the world’s...

According to a 2008 IIASA report, if the world stabilizes at a total fertility rate of 1.5—where Europe is today—then by 2200 the global population will fall to half of what it is today. By 2300, it’ll barely scratch 1 billion.  [it's currently 7 billion]

The reasons for the decline are discussed in the Slate article.

See also this previous post, and this one.