In this talk I present recent work on sub-leading logarithmic corrections to the initial state radiation corrections to the process $e^+ e^- \to \gamma^*/Z^*$ and the calculation of $O(\alpha_s^3)$ corrections to the semileptonic $b \to c$ decay width.
The first calculation is based on the method of massive operator matrix elements and allows to describe the initial state radiation of several processes at future electron-positron colliders at sub-permille accuracy.
The second calculation is based on an expansion in the mass difference of charm and bottom quark. We show the good convergence properties of this series and compare the radiative corrections in different renormalization schemes for the heavy quark masses.
