Theory of rare hadronic decays

In this proceeding we will review the current theoretical status of rare hadronic decays, with a particular focus on decays of the B meson. These decays are indeed excellent indirect probes while searching for New Physics. Given the current experimental situation at colliders, where no new particles have been directly produced, rare decays provide a fundamental and alternative approach in the search for Physics beyond the Standard Model. In particular, the following classes of decays will be here reviewed: Bq → τν, Bq → µµ, B → K(∗)νν¯, B → K(∗)ℓℓ, Bs → ϕℓℓ and b → sγ. We will provide the most updated Standard Model predictions, highlight which are the main sources of uncertainty, and give the current status of New Physics searches in these channels when confronting the theory predictions to current experimental results.