The Epoch of Reionization (EoR) was a cosmic phase transition from a neutral to an ionized state. The first generation of luminous objects were able to heat and ionize their surrounding media, predominantly clouds of neutral hydrogen. Detection of brightness temperature fluctuations from the redshifted hyperfine 21cm line of neutral hydrogen would provide a direct, inherently three-dimensional probe of astrophysics and cosmology during this transformational stage of cosmic history. Foreground power dominates the measurements of interferometers that seek a statistical detection of the EoR. The inherent spectral smoothness of synchrotron radiation -- the dominant foreground emission mechanism -- the chromaticity of the instrument, and the spectral structure of the target signal allows these experiments to delineate a boundary between spectrally smooth and structured emission in Fourier space. These separate components are referred to as the foreground wedge' and the EoR window'. However, Faraday rotation of polarized synchrotron radiation induces frequency-dependent structure in its spectrum, which will leak power from the foreground wedge into the EoR window. This makes polarization a potential contaminant for EoR measurements. This work presents investigations into the impact of polarization on EoR measurements, in the Fourier space relevant to current EoR experiments. We show, separately, both the widest and the deepest integrations on polarized power in the EoR window to date. All results are consistent with negligible leakage, to the noise levels attained. Our deep integration also represents the best limits to date on both polarized and unpolarized power in the EoR window. Polarized redundant calibration is also described and implemented on observations for the first time in this work. We also present new methods to expand the potential of EoR measurements, while remaining within the EoR window paradigm. Interferometric sensitivity to a monopole signal is explored, with the first ever implementations on observational data. We construct higher-order correlation functions to investigate the connection between the kinetic Sunyaev-Zeldovich effect, mapped into Fourier space, and the 21cm power spectrum. Finally, we examine the role deep learning could play in the analysis of more futuristic 21cm image cubes.