Multiloop Corrections to Rare $B$ Decays

Multiloop calculations that matter for low-energy flavour physics are of two generic types. The first-type ones allow us to determine the Wilson coefficients in the effective theory of interest. At the technical level, they can be reduced to evaluating tadpole diagrams. The second-type ones are necessary to express physical observables in terms of the Wilson coefficients. Here, after summarizing the Wilson coefficient status, I am going to describe several recent perturbative calculations that have contributed to a reduction of theoretical uncertainties in the branching ratios of $B_{s,d} \to ℓ^+ℓ^−$ and $\bar{B} \to X_{s,d}γ$