NNLL QCD Corrections to the Decay $B \to X_s \ell^+ \ell^-$

We briefly discuss the status of the NNLL QCD calculations in the inclusive rare $B$ decay $B \rightarrow X_s \ell^+ \ell^-$. Two important ingredients, the two-loop matrix elements of the four quark operator ${\cal O}_2$ and the bremsstrahlung contributions, were quite recently finalised. The new contributions significantly improve the sensitivity of the inclusive decay $B \rightarrow X_s l^+ l^-$ decay in testing extensions of the standard model in the sector of flavour dynamics; for instance the two-loop calculation cuts the low- scale uncertainty in half and the bremsstrahlung calculation leads to a $10 \%$ shift of the position of the zero of the forward- backward asymmetry.