Given the experimental confirmation of the Standard Model (SM) predictions for the discovered Higgs boson as well as the non-observation of signals for beyond-the-Standard Model (BSM) physics in Run-1 and Run-2 of the Large Hadron Collider (LHC), I shall discuss the implications for BSM Higgs models and highlight possible new signatures and search strategies for future LHC runs. After introducing the public tools HiggsBounds and HiggsSignals --- designed to confront BSM models with the experimental results --- I will focus on the Minimal Supersymmetric Standard Model (MSSM) and present a new set of benchmark scenarios specificly designed for upcoming BSM Higgs searches at the LHC. I shall conclude with a brief outlook on the LHC sensitivity in the high-luminosity phase.