A review is given of the nonequilibrium calculation techniques by various authors over the past decade to predict heat fluxes to the windward side of the Space Shuttle orbiter. The results of these techniques are compared with measurements made on the first few flights of the Space Shuttle. The calculations attempt to account for finite rate chemistry in the shock layer around the vehicle and for finite rate catalytic atom recombination on the thermal protection materials. The techniques considered are the axisymmetric viscous shock layer method, three dimensional reacting Euler equation solutions coupled with axisymmetric analog boundary layer method, and a recently developed nonequilibrium 3-D viscous shock layer method
