Lattice $B \to D^{(*)}$ form factors, $R(D^{(*)})$, and $|V_{cb}|$

I discuss recent progress in lattice calculations of $B \to D^{(*)} \ell \nu$ form factors, important for the precision determination of $|V_{cb}|$ in the Standard Model (SM), and for testing SM expectations of lepton flavor universality in observables $R(D^{(*)})$. I also discuss progress in calculations of the related $b \to c$ semileptonic decays $B_s \to D_s^{(*)} \ell \nu$ and $B_c \to J/\psi \, \ell \nu$ now experimentally accessible at the LHC.