This thesis focuses on the signal modelling of Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI) in the brain's white matter (WM). DW-MRI a non-invasive technique with enormous potential for the study of the brain's microstructure by measuring the diffusion properties of biological tissue. In order to infer such microstructure properties from DW-MRI signals --- for example the axon's diameter distribution or the neurite dispersion, just to mention a few --- many models have been proposed in the past decades. However, such models have relied on disregarding several structural components of the WM, like the diameter and direction changes along the axons or the volumetric changes in the tissues' water compartments, which inherently affect the diffusion properties of the studied media. This large heterogeneity in the WM tissue, summed to the high structural variability between different brains regions or WM tracks, have prevented researchers from formulating accurate analytical models to this day.

The following work proposes a paradigm change from the conventional analytic model-based approach to a simulated-based one, centered in the simulation of DW-MRI signals in realistic virtual tissue. Our work starts with the challenge of creating a robust framework for the simulation of DW-MRI as a forward modelling tool for microstructure estimation and continues exploding the simulator capabilities to create a simulation-based microstructure modelling strategy. Each chapter of this thesis presents several contributions to the field for the construction of realistic white matte numerical phantoms, which can later be used for the estimation of the axons' density and diameter distribution, or the design of novel microstructure-specific DW-MRI acquisition sequences. Thus, the contributions presented in this work pave the way for the modelling, study, and validation of complex microstructure models of brain white matter.