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title: Theory overview of semileptonic $B$ decays
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Introduction
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Tree-level semileptonic decays of mesons provide a straightforward way to extract the moduli of several CKM matrix elements, which can then be used to test the CKM matrix unitarity. In the last decade, precision studies of semileptonic $B$-meson decays have been made possible by the the large samples of $B$-mesons collected at the $B$-factories (BaBar and Belle) and at LHCb. At the same time, we witnessed a considerable progress in numerical simulations of QCD on the lattice (LQCD), which nowadays allow us to attain a percent level precision for certain hadronic quantities. For these reasons, semileptonic $B$ decays offer a very promising route to search for the effects of New Physics (NP).

One of the most intriguing results from the $B$-factories and LHC is the indication of lepton flavor universality (LFU) violation, observed in both tree-level and loop-induced semileptonic $B$-decays. The $B$-physics experiments observed a departure from the SM in the tree-level processes, i.e. those mediated by the charged currents, namely,

$$\label{eq:RD-RDst}
R_{D^{(\ast)}} = \dfrac{\mathcal{B}(B\to D^{(\ast)}\tau \bar{\nu})}{\mathcal{B}(B\to D^{(\ast)}l \bar{\nu})}\,,\qquad\qquad l \in \lbrace e,\mu\rbrace\,,$$

which turned out to be $\approx 2-3\,\sigma$ the SM predictions [@Lees:2012xj; @Lees:2013uzd; @Huschle:2015rga; @Aaij:2015yra; @Hirose:2016wfn; @Sato:2016svk; 