The signal discovered in the Higgs searches at the LHC can be interpreted as the Higgs boson of the Standard Model as well as the light CP-even Higgs boson of the Minimal Supersymmetric Standard Model (MSSM). In this context the measured mass value, having already reached the level of a precision observable with an experimental accuracy of about 500 MeV, plays an important role. This precision can be improved substantially below the level of about 50 MeV at the future International Linear Collider (ILC). Within the MSSM the mass of the light CP-even Higgs boson, M_h, can directly be predicted from the other parameters of the model. The accuracy of this prediction should match the one of the experimental measurements. The relatively high experimentally observed value of the mass of about 125.6 GeV has led to many investigations where the supersymmetric (SUSY) partners of the top quark have masses in the multi-TeV range. We review the recent improvements for the prediction for M_h in the MSSM for large scalar top masses. They were obtained by combining the existing fixed-order result, comprising the full one-loop and leading and subleading two-loop corrections, with a resummation of the leading and subleading logarithmic contributions from the scalar top sector to all orders. In this way for the first time a high-precision prediction for the mass of the light CP-even Higgs boson in the MSSM is possible all the way up to the multi-TeV region of the relevant supersymmetric particles. However, substantial further improvements will be needed to reach the ILC precision. The newly obtained corrections to M_h are included into the code FeynHiggs.
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