Spectral domain optical coherence tomography (OCT) is a powerful tool for measuring nanometer-scale displacement responses in the cochlea, as it is capable of volumetric imaging and vibrometry at a depth into a sample. The past decade has seen a wealth of OCT-measured displacement data from structures within the organ of Corti complex (OCC) that had previously been impossible to measure in vivo. These data have revealed surprising features of active intra-OCC motion but have not yet led to a complete understanding of cochlear amplification, the means by which active processes enhance the tuning and gain of the cochlear displacement responses in a level-dependent manner. Certain technical challenges arise from the properties of OCT imaging and vibrometry that obscure the interpretation of intra-OCC displacement measurements. In particular, OCT-measured responses are dependent on the orientation of the system's beam axis. The beam axis is generally chosen based on experimental convenience, and has no inherent relevance to the anatomy of the cochlea. This introduces two problems: 1) OCT-acquired images of the cochlea may be taken at skewed angles relative to the cochlea's naturally endowed anatomical coordinates, and 2) OCT-measured displacement responses are projections of a three-dimensional motion onto the beam axis. This thesis concerns the quantification of these effects on intra-OCC displacement measurements, as well as the development of methods to overcome these complications in vivo. In doing so, previously reported data that appear to disagree can be synthesized. I present a method by which the skew of OCT images relative to cochlear anatomy can be quantified, relating the OCT system's optical coordinates to the cochlear anatomy. With this method, I have shown that OCT images resembling familiar anatomical drawings of longitudinal cross-sections often capture a completely different anatomical slice of the cochlea. This leads to large quantitative shifts in phase responses when measuring displacements along a single beam axis, as opposed to what one would measure if s/he were measuring along an anatomically relevant axis. I have also provided a method by which to account for this phenomenon to capture structures related in some desired anatomical fashion. I then turn to the issue of projection of the three-dimensional cochlear motion onto the OCT beam axis. I have provided a method for reconstructing two- and three-dimensional displacement responses in the relevant anatomical directions by acquiring displacement measurements at multiple locations within the cochlea. In doing so, I have revealed that previously unexplained disagreements between measurements in different experimental preparations can be explained by competing components of motion being projected onto the single axis. I have also shown that motion at the junction between the outer hair cells and Deiters cells follows a lineal pattern, as opposed to non-degenerate elliptical patterns that would be expected of fluid motion in this region. This method requires the acquisition of data at many points within the OCC, making it significantly time-consuming. This makes it vulnerable to sample drift and deterioration, and reduces experimental yield. Certain applications of the method -- such as reconstructing displacement maps over a dense volume -- are thereby intractable. To address this problem, I have developed a compressed sensing method for vibrometry (CSVi). CSVi is a classical optimization method based on a total generalized variation signal prior, which is shown to out-perform methods using total variation and wavelet domain sparsity priors. I have also found that uniform sub-sampling schema offered significant performance benefits over random sub-sampling schema. I found that this CSVi method can reconstruct densely sampled displacement maps in the cochlea in vivo with less than 5% normalized mean square error, using only 10% of samples. While these methods offer new insight into interpretation of OCT displacement measurements, there is still a challenge in measuring the motion of the stereocilia of the hair cells. The stereocilia are too small to be imaged using OCT, and the proxy measurement of differential motion of the reticular lamina and tectorial membrane (between which the stereocilia lie) is not yet achievable in the gerbil base. Stereocilia motion is related to the transduction current through the hair cells, which is critical to understanding cochlear function. These currents lead to neurotransmitter release and active electromotile responses believed to be responsible for cochlear amplification. I present a model for studying another proxy measurement of the stereocilia motion -- the voltage in the cochlea's scala tympani, or cochlear microphonic (CM). This model of CM reveals that to match experimental data 1) stereocilia motion must be more sharply tuned than measured intra-OCC displacement responses, 2) the displacement-current gain of the mechano-electric transducer channels in vivo must be larger than what is measured in vitro by a factor of ~6, and 3) the hair cells at more basal locations of the cochlea must be compromised. These predictions offer insight into aspects of cochlear mechanics that are not easily probed using OCT.