X-ray phase-contrast tomography is a powerful tool to dramatically increase the visibility of features exhibiting a faint attenuation contrast within bulk samples, as is generally the case of light (low-Z) materials. For this reason, the application to clinical tasks aiming at imaging soft tissues, as e.g., breast imaging, has always been a driving force in the development of this field. In this context, the SYRMA-3D project, which constitutes the framework of the present work, aims to develop and implement the first breast computed tomography system relying on the propagation-based phase-contrast technique at the Elettra synchrotron facility (Trieste, Italy). This thesis finds itself in the ‘last mile’ towards the in-vivo implementation, and the obtained results add some of the missing pieces in the realization of the project. The first part of the work introduces a homogeneous mathematical framework describing propagation-based phase contrast from the sample-induced X-ray refraction, to detection, processing and tomographic reconstruction. The original results reported in the following chapters include the implementation of a pre-processing procedure dedicated for a novel photon-counting CdTe detector; a study, supported by a rigorous theoretical model, on signal and noise dependence on physical parameters such as propagation distance and detector pixel size; hardware and software developments for improving signal-to-noise ratio and reducing the scan time; and, finally, a clinically-oriented study based on comparisons with clinical mammographic and histological images. The last part of the thesis attempts to widen the experimental horizon: first, a quantitative image comparison of the synchrotron-based setup and a clinically available breast-CT scanner is presented and then a practical laboratory implementation is detailed, introducing a monochromatic propagation-based micro-tomography setup making use on a high-power rotating anode source.