Beyond standard model Higgs physics: prospects for the High Luminosity LHC

This article summarizes a talk given at Higgs Hunting 2014 on projections of the sensitivity of the ATLAS and CMS experiments to beyond Standard Model Higgs physics at the High Luminosity Large Hadron Collider. We describe results on vector boson scattering, searches for additional neutral Higgs bosons in two Higgs doublet models and flavour changing neutral current top decays.