It is unsustainable; the world's stock of food is crashing. Fish & other sea food is on the brink. Tuna is now so over harvested that it will likely become extinct in the very near future, wild salmon as well along with many other species.
Overfishing is resulting in algae blooms which are in turn triggering jellyfish blooms which will devour the fry of fish that do manage to breed. This is already a big problem off Japan and it is spreading.
In Africa fish harvest is down over 70% from a decade ago. They have decimated wild game and many species are barely hanging on. Look at the size of the seasonal migration masses.
There will be a massive reduction in population by some means in the near future. But it is hard to say what form it will come in.
China is trying to reduce their population with the one child law. For many years it really only applied to the poor more urban Chinese. There was an allotment for peasant farmers in the countryside and the rich just paid a fine. But they have moved to remedy this and make it apply to everyone now.
Americans would be wise to go and live in an overpopulated country before encouraging further immigration, it isn't a pretty picture.
The US reached ZPG in 1998 at 220 million. there are now 320 million and the growth has been entirely through immigration.
The planet can sustain about 1/2 of what we have in theory. But that would be assuming that the resources exist that did when we passed the 3 billion mark, that isn't going to happen.