Liquid xenon has been used with great success in recent attempts to directly detect dark matter particles. The Large Underground Xenon (LUX) experiment recently concluded nearly four years of underground operations at the Sanford Underground Research Facility in Lead, South Dakota. The final 332 live-days of data were acquired with time-varying detector conditions, which required frequent calibrations and new data quality studies beyond those used for the results from the initial 95-live-day exposure. In addition to its world-leading dark matter search at low recoil energies approaching 1 keV, the LUX experiment has been used for the study of liquid xenon properties out to near 1 MeV. New measurements of scintillation and ionization yields and electron-ion recombination in liquid xenon were made, and a treatment of high-energy detector effects, including saturation and multiple-scatter rejection, was implemented for improved energy resolution. These improved analysis techniques have been used to set a new limit on the half-life for the neutrinoless double-beta decay candidate, Xe-134. The sensitivity of searches for rare events, like dark matter interactions and neutrinoless double-beta decay, scale with target mass, and so the design and successful construction of a 200-kV cathode high voltage system, applicable for future ton-scale noble liquid detectors like LUX-ZEPLIN (LZ), is also described.