  We compute corrections of order $\alpha_s^3$ to the decay $b \to c \ell
\bar\nu$ taking into account massive charm quarks. In the on-shell scheme large
three-loop corrections are found. However, in the kinetic scheme the three-loop
corrections are below 1\% and thus perturbation theory is well under control.
We furthermore provide results for the order $\alpha_s^3$ corrections to $b \to
u \ell \bar\nu$ and the third-order QED corrections to the muon decay which
will be important input for reducing the uncertainty of the Fermi coupling
constant $G_F$.
