The LUX collaboration new results advance the search for dark matter candidate particles in the 4 GeV/c^2 and higher mass range, with a maximal spin-independent 90% C.L. limit of 2 x 10^-46 cm^2 at 50 GeV/c^2 for its 332 live-day run, following after 6 x 10^-46 cm^2 cross-section for 33 GeV/c^2 mass from the re-analysis of its initial 95 live-day WIMP search data from December 2015. LUX has performed multiple advanced in situ neutron and beta/gamma calibrations of light and charge yields down to 1.1 and 0.7 keV, respectively, in nuclear recoil energy and 1.3 and 0.2 keV in units of electron recoil energy, thereby bypassing the past practice of extrapolating yields from ex situ calibrations or simulation models alone. For this conference proceedings, consequences of the new calibrations for the limit on the interaction cross-sections for low-mass WIMPs will be highlighted. Previous claims of a WIMP signal, from other detectors, are now even more strongly disfavored, assuming isospin invariance and the standard WIMP halo model. Both spin-independent and spin-dependent limits will be discussed, including the recent completion of LUX's 332-live-day blind run. Lastly, we highlight the conceptual design and future plan for its 10-ton-scale, next-generation successor LZ, which plans on achieving less than 3 x 10^-48 cm^2 sensitivity for a WIMP of mass 40 GeV/c^2.