Theory overview of tree-level $B$ decays

Abstract

I describe the theoretical progress in the study of semileptonic tree-level B decays, and its interplay with recent experimental results. In particular, I focus on two anomalies: the ratios $R(D^{(*)})=\displaystyle\frac{{\cal B}(B \to D^{(*)} \tau \bar \nu_\tau)}{{\cal B}(B \to D^{(*)} \ell \bar \nu_\ell)}$ and the inclusive versus exclusive determination of $|V_{cb}|$. I review a few explanations proposed for such anomalies, and discuss tests to shed light on their origin.