The objective of this thesis is to explore the unique capabilities of quantitative oblique back-illumination microscopy (qOBM), a novel tomographic, label-free, non-invasive, real-time, and affordable quantitative phase imaging (QPI) technology. The aim is to develop new qOBM-based optical and computational pipelines to warrant a more widespread use of this technology for biomedical applications. qOBM overcomes QPI's restriction to thin samples, and enables high contrast and high-resolution quantitative phase imaging of thick biomedical samples with cross-sectional and tomographic capabilities, providing valuable morphological and biophysical information about the imaged specimen. In this work, we first explore the application of qOBM in two clinical and biomedical areas, including the viability assessment of umbilical cord blood units for banking as well as surgery and pathology assistance in the detection of brain tumor regions. Necessary modifications to the optics and image analysis tools are presented in each of the aforementioned applications. Second, we propose adapting qOBM for the non-invasive study of cellular and sub-cellular structural dynamics in 3D cell cultures. We again consider various optical and computational modifications to the system required to capture fast biological processes, and present data analysis pipelines to produce functional images of unlabeled live samples. Lastly, we demonstrate a deep learning single-capture approach to further simplify and improve the system's applicability. Overall, the work presented in this dissertation seeks to establish the impact of qOBM within the realm of biomedical optics. We do so by enhancing this technology's accessibility and effectiveness in a broad range of applications through modified optical designs and advanced computational approaches. We expect this work to pave the way for the development of novel label-free platforms for clinical and biomedical purposes.