  $B$ anomalies play a prominent role in Beyond the Standard Model (BSM)
physics searches. In particular, the long standing tension between the
inclusive and the exclusive determinations of the CKM matrix element $|V_{cb}|$
and the current tensions in the $R(D)$--$R(D^\ast)$ plane between theory and
experiment have brought the $B\to D^{(\ast)}\ell\nu$ semileptonic processes to
the spotlight. Existing lattice-QCD calculations of the $B\to D\ell\nu$ form
factors at non-zero recoil are being complemented with very recent developments
in the $B\to D^\ast\ell\nu$ channel. In this review I discuss recent progress
in lattice calculations of $B\to D^{(\ast)}\ell\nu$, as well as the
implications of these results for high precision determinations of $|V_{cb}|$
and the Lepton Flavor Universality (LFU) ratios $R(D^{(\ast)})$.
