Mixing and combustion of supersonic reacting flows are currently under investigation for new generation launchers and trans-atmospheric vehicles. Experimental results with hydrogen injected at Mach 2.5 in a Mach 2 airstreams showed combustion taking place just in ∼0.6 m: this indicates that supersonic combustion is very efficient. A criterion to estimate an adequate combustor length to anchor flame has been developed based on a characteristic mixing function, M.F. This criterion has been found to be satisfied by the present NASA-Langley test case. Numerical simulations of the same test case have also been done to better understand physics of supersonic reacting flows. These simulations have included the subgrid scale model, ISCM, developed appositely for supersonic combustion. This model takes into account the effect of compressibility on reaction rate and on mixing. Numerical simulations have pointed out that the flame is unsteady: it anchors at about 15 cm from the injector, develops downstream and lifts off. Periodical ignition and quenching have been investigated.