Combustion produces more than 80 percent of the world’s energy. This will continue for a long time as the global energy growth remains much larger than what new renewable energies can provide. Our civilization must allow the growth of combustion sources but, at the same time, keep global warming as well as pollution under control. Science has a key role in this scenario: it must optimize combustion systems far beyond the present state of the art. To do this, one promising path is to use High Performance Computation to compute and optimize combustors before they are built. This talk focuses on aerospace propulsion where optimization often leads to the occurrence of instabilities where combustion couples with acoustics, leading to unacceptable oscillations (the most famous example is the Apollo engine which required 1330 full scale tests to reach acceptable oscillation levels). The talk will show how simulation is used to control these problems, in real gas turbine engines and in rocket engines.