The new particle discovered at the LHC can be interpreted as the lightest CP-even Higgs boson of the Minimal Supersymmetric Standard Model (MSSM), where Mh denotes its mass. The experimental precision of this mass has reached the level below ∼ 500 MeV. In the MSSM Mh can directly be predicted from the other parameters of the model. The accuracy of this prediction should at least match the one of the experimental result. The relatively high mass value of about 125 GeV has led to many investigations where the scalar top quarks are in the multi-TeV range. We review the recent improvement in the prediction for Mh in the MSSM that has been reached 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.