In this talk, I will review the current status of Higgs sector of MSSM in light of the latest 13 TeV LHC data. I will also discuss the possibility to search the MSSM heavy Higgses through the cascade decay of electroweakinos, in the mono-Z+MET, mono-W+MET and 3l+MET final states. I will also present the results from our study of the decay of 125 GeV Higgs boson to light LSP neutralino in MSSM in the context of collider searches and astrophysical experiments. Moreover, I will revisit the SM non-resonant di-Higgs searches and briefly discuss the ramifications of varying the Higgs self-coupling on the optimized di-Higgs search strategies. Finally, I will present the HL-LHC projections for resonant heavy Higgs searches in the di-Higgs, ttbar and bbH/A search channels, and review their impact on the Higgs sector of MSSM.