Liquid fuel rocket engines using H2/O2 combustion are again a major research theme in Europe especially for the future Ariane 6 rocket. This talk will present recent progress in two critical mechanisms controlling combustion in cryogenic H2/O2 rocket engines. (1) the stabilization zone of the H2/O2 flame on the lips of a coaxial injector will be studied using DNS with full chemistry and a dual resolution of heat transfer within the splitter plate of the injector. (2) the first full LES of a complete rocket engine installed at DLR Lampoldshausen will be described. Using LES and a simplified chemical model, this simulation allows to capture and identify the two strongest modes (10 and 20 kHz) appearing in this 100 MW engine. Comparisons with experiments show that LES is able to discriminate between stable and unstable regimes.