  A review is given on the quantum correction $\Delta r$ in the $W$--$Z$ mass
correlation at the electroweak two-loop level, as derived from the calculation
of the muon lifetime in the Standard Model. Exact results for $\Delta r$ and
the $W$-mass prediction including ${\mathcal{O}}(\alpha^2)$ corrections with
fermion loops are presented and compared with previous results of a
next-to-leading order expansion in the top-quark mass.
