Theory of rare B meson decays

I review the NLO QCD calculations of the branching ratio for B--> X_s gamma in the SM. Including the leading electromagnetic corrections, one obtaines BR(B-> X_s gamma)=(3.32 +- 0.30)*10^{-4}. Confronting theory with the newest data, an updated value for |V_{ts}| is obtained: |V_{ts}|=0.037 +- 0.007. Theoretical progress on the photon energy spectrum is also discussed. The inclusive FCNC semileptonic decays in the SM are briefly summarized. Furthermore, B--> X_s gamma is considered in 2HDMs and in different SUSY scenarios. QCD corrections are shown to be crucial.