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.