  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.
