The groundbreaking observation of neutrino oscillations indicates that the elusive neutrino is massive, providing tantalising evidence for physics beyond the standard model. However, given that neutrinos cannot obtain mass through the same mechanism as the charged leptons, unsolved problems still remain. Neutrinoless double beta decay (0νββ) is a hypothetical process that, if discovered, may shine light on the origins of neutrino mass. It would also confirm that Majorana fermions exist in nature, and that the neutrino is its own anti-particle, demonstrating that lepton number is not conserved through a fundamental symmetry of the universe. In this thesis, the capability of past, present and future dual-phase xenon time projection chambers to search for 136Xe 0νββ is demonstrated. A search for this process is performed in a short 19 kg·yr exposure of the LUX experiment, with the goal of illustrating the reconstruction of O(MeV) events in such detectors, and demonstrating the techniques required for future experiments. Next, the sensitivity of the LUX-ZEPLIN (LZ) experiment to the 0νββ half-life T1/2 is studied, revealing that after 1,000 days of exposure, LZ can exclude T1/2 < 1.06 × 1026 yr at 90% CL. A similar sensitivity projection is also performed for a hypothetical, large scale future detector that utilises O(100 tonnes) of xenon. It is shown that at this scale it is possible to exclude T1/2 < 1.0 × 1028 yr, and probe almost the entire inverted neutrino mass hierarchy at 90% CL. Finally, a machine learning method for fast simulation of the detector response using a generative adversarial network is studied. It is demonstrated that this technique can accurately generate the digitised photomultiplier signals resulting from interactions in a dual-phase detector. This technique may provide a computationally inexpensive method for fast simulation in future detectors.