So far as I've heard, human consumption is unsustainable. In practice, that seems to mean either (1) we are consuming resources (such as petroleum) that cannot be replaced and will sooner or later be exhausted, or (2) we are consuming resources (such as many species of fish) faster than they be replaced.
If those things are true (and very few scientists who have studied the matter would say they are not the case), then we are most likely headed for a population collapse at some point. That's to say, our current population levels seem to be dependent on unsustainable consumption.
In theory I guess, everyone on earth could voluntarily cut back to a sustainable level of resource consumption -- and that might solve the problem without a population collapse -- but that's mere theory. In practice, it won't happen. Americans, for instance, are not going to willingly cut back their consumption of the earth's resources.