$B$ 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 $R(D^{(\ast)})$.