Transient combustion processes occur in gas turbine combustion chambers operated close to the blow-out limit, or under changing loads. Some low-emission combustion concepts also have a strong tendency to produce unwanted combustion oscillations. Fluid-mechanical instabilities play a major role in this regard, as does the interaction of acoustic pressure fields with flow and combustion inside the combustion chamber. Numerical simulation of combustion oscillations poses major challenges not only for the numerical methods applied, but also for turbulence and combustion models, as well for the modelling of boundary conditions. Further research is essential.