An overwhelming majority of matter in the Universe is dark matter, a substance unlike anything we know. Detecting dark matter particles requires ruling out observed phenomena caused by known particles. This thesis advances efforts toward the detection of dark matter using one of the most sensitive particle detection technologies: the dual-phase liquid xenon time projection chamber. Specifically, data from the XENON1T Experiment, located in Italy, and the Purdue small-scale ASTERiX detector are analyzed. A background of Lead-214 beta decay events can be mitigated by tracing the radioactive Radon-222 decay chain in XENON1T. However, a preliminary reduction of background has a high cost to exposure. Research on several topics was conducted with Purdue undergraduates, including a search for dark matter particles up to the Planck Mass, characterizing backgrounds due to muons, and searching for Boron-8 solar neutrino signals. XENON1T single-scatter dark matter limits were extended to a particle mass of 10¹⁸GeV/c². The ASTERiX detector was modified to characterize a significant background to the smallest detectable energy signatures: single- and few-electron ionization signals. Infrared light was determined to be ineffective at reducing this background, and their rates were observed to decrease inversely with time since an energetic interaction according to a power law. The rates of single- and few- electron backgrounds increase linearly with increased applied extraction fields and increased depth of the initial interaction in the detector. These results indicate that these backgrounds originate at the liquid-gas interface of dual-phase detectors. In exploring a single-photon threshold for initial scintillation signals, a previously unconsidered background of large dark count signals in the photosensors became apparent. The high background of small ionization signals and large dark count signals deterred a search for Boron-8 solar neutrino interactions in XENON1T. These studies are vital to mitigating backgrounds and improving the sensitivity of liquid xenon time projection chambers to new physical phenomena.