We'll not really run out of most resources since...
Fossil fuel wise we'll move to renewable, when push comes to shove it'll be amazing just how quickly former petroleum companies come out with much more highly efficient green energy sources, almost like they were sitting on them. Solar is already cheaper than coal for many countries and has a lot of improvements to generate more power per sq metre in the pipeline. Then of course there's nuclear
Metals and plastics we can recycle for the most part, again when it comes to it we'll obviously put much more effort into recycling thoroughly.
Main thing would be other uses for petroleum products, but we'd find alternatives. Some bacteria can be made to produce them for instance.