  Predictions for the Higgs masses are a distinctive feature of supersymmetric
extensions of the Standard Model, where they play a crucial role in
constraining the parameter space. The discovery of a Higgs boson and the
remarkably precise measurement of its mass at the LHC have spurred new efforts
aimed at improving the accuracy of the theoretical predictions for the Higgs
masses in supersymmetric models. The "Precision SUSY Higgs Mass Calculation
Initiative" (KUTS) was launched in 2014 to provide a forum for discussions
between the different groups involved in these efforts. This report aims to
present a comprehensive overview of the current status of Higgs-mass
calculations in supersymmetric models, to document the many advances that were
achieved in recent years and were discussed during the KUTS meetings, and to
outline the prospects for future improvements in these calculations.
