There are only two options. 1: Humanity, and the rest of life, gets wiped out because of our inability to control the world we created. Or 2: We learn to live with what we have, stabilize, and prosper while keeping net change at a minimum or to a better degree.
I believe that the second option is much, much more likely than the first. I may sound like an optimist, but I am looking at it this way:
As one of many evolved species, we humans have a very strong sense of self preservation. The only reason why humanity is not in a nuclear apocalypse right now is because everyone are too afraid to face it. And it is this fear that will also save us, and the planet.
Right now it is the "hippy happy" thing to try and save the planet. I hope it won't come to it, but eventually, even the greediest, most selfish petrol-head wasteful consumer out there will figure out that they have to go green and save the world. If only because their own skin depends on it.
So the reason might be somewhat cynical, but yes, we will survive.