The problem is our (relatively) recent invention of civilization, of course. I mean cities, the system of concentrating populations and resources. A given population with certain living standards is going to need a steady stream of raw materials and produce a certain amount of waste products. The problem has been around since we built the first city.
What to do about it? Well, the world's population is not going to abandon its cities and system of living we call civilization. It's simply not going to happen, in spite of what the more radical environmental pundents might want. We can slow down the growth somewhat, and do some tweaking of the system to mitigate the worst pollution, but we're not going to stop consuming and creating waste. That's the reality of human nature. We breed. We try to acquire higher standards of living. We find cures for disease and try to live longer. That's not going to change.
So we either use our intelligence to find solutions to the problems our civilization is causing, or maybe one day the system will collapse. Then the problem is solved for us. Certainly we know some solutions, but they're hardly acceptable. Eliminate population on our own? Force nations to stop developing and roll back the standard of living the leading nations now enjoy? Yea, right.
In the end, civilization might be considered a system of living with a fatal flaw. But that will be a lesson for future generations.