Diffusion of water molecules in biological tissues depends on several microstructural properties. Therefore, diffusion Magnetic Resonance Imaging (dMRI) is a useful tool to infer and study microstructural brain changes in the context of human development, ageing and neuropathology. In this thesis, the state-of-the-art of advanced dMRI techniques is explored and strategies to overcome or reduce its pitfalls are developed and validated. Firstly, it is shown that PCA denoising and Gibbs artefact suppression algorithms provide an optimal compromise between increased precision of diffusion measures and the loss of tissue’s diffusion non-Gaussian information. Secondly, the spatial information provided by the diffusion kurtosis imaging (DKI) technique is explored and used to resolve crossing fibres and generalize diffusion measures to cases not limited to well-aligned white matter fibres. Thirdly, as an alternative to diffusion microstructural modelling techniques such as the neurite orientation dispersion and density imaging (NODDI), it is shown that spherical deconvolution techniques can be used to characterize fibre crossing and dispersion simultaneously. Fourthly, free water volume fraction estimates provided by the free water diffusion tensor imaging (fwDTI) are shown to be useful to detect and remove voxels corrupted by cerebrospinal fluid (CSF) partial volume effects. Finally, dMRI techniques are applied to the diffusion data from the large collaborative Cambridge Centre for Ageing and Neuroscience (CamCAN) study. From these data, the inference provided by diffusion anisotropy measures on maturation and degeneration processes is shown to be biased by age-related changes of fibre organization. Inconsistencies of previous NODDI ageing studies are also revealed to be associated with the different age ranges covered. The CamCAN data is also processed using a novel non-Gaussian diffusion characterization technique which is invariant to different fibre configurations. Results show that this technique can provide indices specific to axonal water fraction which can be linked to age-related fibre density changes.