Astronomical and cosmological observations on different scales point to the existence of dark matter. In the current cosmological paradigm this dark matter accounts for about 26% of the energy-density of the universe, yet has not been directly observed. Weakly Interacting Massive Particles (WIMPs) and axions are two candidates among the many theories and particles proposed to explain dark matter. Direct detection experiments aim to detect the scattering or coupling of dark matter to the detector medium. The event rate in such experiments is expected to exhibit an annual modulation due to the motion of the Earth through the Galactic dark matter halo. The XENON collaboration built several experiments that have searched for WIMP dark matter by looking for WIMPs scattering on xenon nuclei. The heart of these detectors consists of a Time Projection Chamber (TPC) which records the scintillation light (S1) and ionization charge (S2) signal following a recoiling xenon nucleus as well as its position and time. Using these ultra-low background detectors, the XENON collaboration has set world-leading exclusion limits on the WIMP-nucleon scattering cross-section. In this thesis several different ways of enhancing direct detection experiments are presented, involving time dependent signal models, event reconstruction and a method enhancing statistical inference. First, during a search for event rate modulation, spanning almost 4 years of XENON100 data, no oscillation was found to be compatible with the expected signature. This thesis presents a verification of the correctness of the test statistic distribution used in this analysis using dedicated simulations. Second, the positions of interactions in XENON detectors are used for detector volume fiducialization as well as for modeling the position dependent detector response. This thesis presents the position reconstruction methods used during the first XENON1T science analysis. Third, a new algorithm for position and energy reconstruction using the likelihood-free paradigm is presented. This simulator-based method increases the accuracy of the previous method by up to 15% and can simultaneously infer the transverse position and size of the charge signal. Fourth, to enhance the physics reach of future dark matter searches using xenon TPCs, a new method for computing differential rates is developed. This method replaces the calculation usually performed by Monte-Carlo simulations with an equivalent analytic expression. This enables the use of higher dimensional explicit (profile) likelihood functions, resulting in better signal-background discrimination. The new method uses time dependent signal models (encoding annual modulation) as well as spatially non-uniform sources such as a radiogenic neutron background and fully accounts for the non-uniform detector response. This method can significantly reduce the exposure needed for a potential dark matter discovery in future detectors such as XENONnT. Lastly, the amplitude of the axion dark matter field is expected to exhibit stochastic behavior. Experiments whose measurements are shorter than the coherence time of the field need to include this effect in their data analysis and inference. This thesis presents an analysis of a simulated axion signal in a CASPEr-ZULF-like detector, showing that exclusion limits on the axion amplitude are too strong by a factor ~4 when not including the axion amplitude fluctuation.