They are headed in the right direction:

India - Total Fertility Rate

With the exception of some dangerous places in Central America, the Americas are essentially at replacement level fertility rates. Europe and East Asia are below replacement levels. In fact the only large area with a high fertility rate is Africa.

If Africa can get improved economies, health and education levels they too will be on the path of the rest of the earth. This will result in a peak world population just below ten billion some time late in the century, followed by a slow decrease in population into the future.

What can upset this is unknowns: pandemics, wars and bad governments. I'm not talking about democracies here but truly corrupt oligarchies and dictatorships.