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Direct searches for dark matter (DM) by the LUX and PandaX-II Collaborationsemploying xenon-based detectors have recently come up with the most stringentlimits to date on the spin-independent elastic scattering of DM off nucleons.For Higgs-portal scalar DM models, the new results have precluded anypossibility of accommodating low-mass DM as suggested by the DAMA and CDMS IISi experiments utilizing other target materials, even after invokingisospin-violating DM interactions with nucleons. In the simplest model, SM+D,which is the standard model plus a real singlet scalar named darkon acting asthe DM candidate, the LUX and PandaX-II limits rule out DM masses roughly from4 to 450 GeV, except a small range around the resonance point at half of theHiggs mass where the interaction cross-section is near the neutrino-backgroundfloor. In the THDM II+D, which is the type-II two-Higgs-doublet model combinedwith a darkon, the region excluded in the SM+D by the direct searches can berecovered due to suppression of the DM effective interactions with nucleons atsome values of the ratios of Higgs couplings to the up and down quarks, makingthe interactions significantly isospin-violating. However, in either model, ifthe 125-GeV Higgs boson is the portal between the dark and SM sectors, DMmasses less than 50 GeV or so are already ruled out by the LHC constraint onthe Higgs invisible decay. In the THDM II+D, if the heavier $CP$-even Higgsboson is the portal, theoretical restrictions from perturbativity, vacuumstability, and unitarity requirements turn out to be important instead andexclude much of the region below 100 GeV. For larger DM masses, the THDM II+Dhas plentiful parameter space that corresponds to interaction cross-sectionsunder the neutrino-background floor and therefore is likely to be beyond thereach of future direct searches without directional sensitivity.

New LUX and PandaX-II Results Illuminating the Simplest Higgs-Portal Dark Matter Models