A 2012 article in Scientific American quotes Dennis Meadows and Jorgen Randers (it’s a little unclear which is speaking when) on how they think a collapse will play out:

For the coming few decades, Randers predicts, life on Earth will carry on more or less as before. Wealthy economies will continue to grow, albeit more slowly as investment will need to be diverted to deal with resource constraints and environmental problems, which thereby will leave less capital for creating goods for consumption. Food production will improve: increased carbon dioxide in the atmosphere will cause plants to grow faster, and warming will open up new areas such as Siberia to cultivation. Population will increase, albeit slowly, to a maximum of about eight billion near 2040. Eventually, however, floods and desertification will start reducing farmland and therefore the availability of grain. Despite humanity’s efforts to ameliorate climate change, Randers predicts that its effects will become devastating sometime after mid-century, when global warming will reinforce itself by, for instance, igniting fires that turn forests into net emitters rather than absorbers of carbon. “Very likely, we will have war long before we get there,” Randers adds grimly. He expects that mass migration from lands rendered unlivable will lead to localized armed conflicts…

Meadows holds that collapse is now all but inevitable, but that its actual form will be too complex for any model to predict. “Collapse will not be driven by a single, identifiable cause simultaneously acting in all countries,” he observes. “It will come through a self-reinforcing complex of issues”—including climate change, resource constraints and socioeconomic inequality. When economies slow down, Meadows explains, fewer products are created relative to demand, and “when the rich can’t get more by producing real wealth they start to use their power to take from lower segments.” As scarcities mount and inequality increases, revolutions and socioeconomic movements like the Arab Spring or Occupy Wall Street will become more widespread—as will their repression.