Heavy Quark Production at High Energy

We report on QCD radiative corrections to heavy quark production valid at high energy. The formulae presented will allow a matched calculation of the total cross section which is correct at $O(\as^3)$ and includes resummation of all terms of order $\as^3 [\as \ln (s/m^2)]^n$. We also include asymptotic estimates of the effect of the high energy resummation. A complete description of the calculation of the heavy quark impact factor is included in an appendix.