The white matter of the brain contains all the connections between different parts of the grey matter. Many diseases especially affect the brain’s white matter. For instance, the white matter tracts are destroyed in neurodegenerative diseases, such as Alzheimer’s disease. Accordingly, there is a large interest in features of the white matter to understand the pathophysiological mechanisms underlying these diseases. Diffusion MRI enables non-invasive characterization of the white matter architecture by measuring features of local diffusion processes. Importantly, the diffusion is larger along white matter tracts rather than perpendicular to them due to structural hindrance of the myelin sheets that surround nerve cells. Diffusion MRI measures the diffusion in a large number of directions to yield so-called diffusion weighted images (DWI’s). Conventionally, the diffusion is modelled from the DWI’s by a single ellipsoidal shape, mathematically termed a tensor. Such a tensor reflects the principal directions of diffusion and the associated diffusion lengths. Typically, measures such as the imbalance in diffusion, i.e. the so-called fractional anisotropy, and the mean diffusivity, are calculated from the diffusion tensor to characterize the white matter. However, a single tensor is not appropriate for two-way and three-way crossings of tracts. The goal of this thesis was to improve the modelling of more complex diffusion shapes. Therefore, a multi-tensor is used. However, a pitfall with such a complicated model is that it is prone to ‘overfitting’, for instance as a dual tensor model is fit to single tract data. In that case, the estimated diffusion features will be inaccurate and/or imprecise. The methods in this thesis aim to adapt the model to the underlying structures: a single tensor for single fiber data and dual tensors for fiber crossings. While doing so, the techniques must cope with different measurement circumstances, for instance a varying signal to noise ratio. Initially, two different frameworks are proposed to structure adaptively determine diffusion parameters. The first framework (Chapter 2) involves a so-called automated relevance determination (ARD) approach to estimate the parameters of a dual tensor model. The dual-tensor model automatically adapts to single fibers by reducing one of the volume fractions to a near zero value in case there is no support for a second tensor in the data. It is demonstrated that the ARD approach gives a higher sensitivity in detecting age-related white matter atrophy than standard techniques. A limitation of the ARD framework is that the employed dual-tensor model primarily aims to characterize two-way crossings and simpler configurations. Recent studies reported evidence for the existence of a three-way crossing of fiber bundles. The second framework (Chapter 3) relies on a maximum a-posteriori (MAP) estimator to characterize the diffusion in three-way crossings based on a triple-tensor model. A new model selection technique quantifies the extent to which candidate models are appropriate, i.e. single-, dual- or triple-tensor model. The MAP estimator combined with the model selector is shown to enhance the precision of the parameter estimation, without decreasing the accuracy. The proposed framework improved the sensitivity of statistical analysis of differences between left and right-handed subjects from a large a publically accessible dataset. Unfortunately, the estimation of complex diffusion models is often hampered by a low signal to noise ratio (SNR) of the underlying DWI data. Therefore, two methods are studied to filter the data in order to improve the SNR and in turn enhance the estimation of the diffusion properties. At first (Chapter 4), we propose a structure-adaptive technique to suppress the noise in the underlying DWI data. Initially, the DWI data is decomposed into compartment-specific contributions. Subsequently, these contributions are filtered, after which noise suppressed data is reconstructed from the filtered contributions. Finally, the noise-suppressed DWI data is used to estimate the parameters of a complicated dual tensor model. The results demonstrate that noise limits the regions with significant differences between two age groups. Instead, subtle differences are identified after filtering. Secondly, a method is introduced to estimate a multi-tensor model from the unfiltered diffusion data after which denoising is performed by filtering the tensors (Chapter 5). The method restricts the denoising to tensors of the same population, even in complex fiber structures, such as crossings and touching fiber bundles. An analysis on the correlation between white matter atrophy and age demonstrates that this enables more sensitive detection of changes in white matter properties. In conclusion, this thesis improves the accuracy and the precision of the estimation of diffusion properties by carefully modelling complex fiber structures based on multi-tensor representations. What is more, it enhances the estimation by filtering the data to suppress the noise on the data. We anticipate that many diffusion MRI studies can benefit from this work.