Present Status of Inclusive Rare $B$ Decays

We give a status report on inclusive rare B decays, highlighting recent developments and open problems. We focus on the decay modes $B \to X_{s,d} \gamma$, $ B \to X_s \ell^+\ell^-$ and $B \to X_s \nu \bar \nu$ and on their role in the search for new physics. Most of the inclusive rare B decays are important modes of flavour physics due to the small hadronic uncertainties. They can be regarded as laboratories to search for new physics. We collect the experimental data already available from CLEO and the $B$ factories BABAR and BELLE. We review the NLL and NNLL QCD calculations of the inclusive decay rates that were recently completed, and discuss future prospects, especially the issue of the charm mass scheme ambiguity. Finally, we analyse the phenomenological impact of these decay modes, in particular on the CKM phenomenology and on the indirect search for supersymmetry. We also briefly discuss direct CP violation in inclusive rare B decays, as well as the rare kaon decays $K^+\to \pi^+\nu\bar{\nu}$ and $K_L \to \pi^0 \nu \bar{\nu}$, which offer complementary theoretically clean information.