Rare B decays at LHCb

Rare loop-induced decays are sensitive to New Physics in many Standard Model extensions. In this paper we discuss the potential of the LHCb experiment to very rare $\mathrm{B_s} \to \mu^+ \mu^-$ decays, radiative penguin $\mathrm{b \to s}\gamma$ decays and electroweak penguin $\mathrm{b \to s\ell\ell}$ decays. The experimental strategies and the expected sensitivities are presented.