Magnetic Resonance Imaging (MRI) is a flexible medical imaging technique that facilitates measurement of a wide range of contrasts particularly in soft tissue (e.g. brain and heart). Conventionally, qualitative images are acquired in which certain physical tissue properties are emphasized such as the transverse and longitudinal relaxation times. Such images are frequently referred to as "weighted", i.e. T1-weighted. Quantitative MRI (qMRI) aims at measuring the underlying tissue parameters governing the contrast instead of yielding mere weighted images. These quantitative parameter estimations were proven to be more reproducible than conventional MR images and more sensitive to certain disease processes, enabling enhanced longitudinal comparisons within subjects as well as comparisons between subjects. MR Fingerprinting (MRF) is an example of such a quantitative technique. MRF uses a combination of transient state acquisitions with varying flip angle patterns, severe undersampling and advanced signal models to allow for fast qMRI acquisitions and accurate estimation of a wide range of parameters. While most qMRI methods assume a single tissue type per voxel, this is almost never a valid assumption. This assumption especially breaks down at tissue boundaries or when tissues consist of multiple, mixed compartments, such as water contained between myelin sheets in the brain, often called myelin water surrounded by extra-cellular water. The goal of this thesis is to develop enhanced methodology for quantitative MRI by extending traditional signal and image post-processing methods. Specifically, the focus is on MR Fingerprinting in combination with multi-component estimations, in which different compartments are included in a mixed estimation model. This is done to obtain more information from the acquired data and to improve quantification, therefore possibly obtain new clinical insights. Important steps towards clinical use are to enhance estimation accuracy and precision compared to previous methods and reduce the scan time. In this thesis the Sparsity Promoting Iterative Joint NNLS (SPIJN) algorithm is proposed for obtaining multi-component estimations from MRF data. This enabled sub-voxel, fractional estimation of signal components in a region of interest, without making a priori assumptions about tissues expected to be present. The main novelty of this method is to combine a non-negativity with a joint-sparsity constraint that limits the total number of tissues identified in a region of interest. As a result it became possible to obtain magnetization fraction maps of the white matter, gray matter, CSF and a component with shorter relaxation times related to myelin water. The repeatability of the proposed method is studied in 5 subjects that were scanned 8 times with one week in between the scans each time. Comparison of the obtained white matter, gray matter and CSF maps with segmentations from conventional methods shows high repeatability of the estimated relaxation times and more fine structures in the CSF magnetization fraction maps. Additionally, the proposed SPIJN algorithm was applied to data from a more conventional qMRI sequence, i.e. a multi-echo spin-echo sequence, to obtain estimations of the so-called myelin water fraction in the brain. The resulting images show significantly improved noise robustness compared to the standard multi-component analysis method, improving the usability. MRF scans can be acquired in a relatively short acquisition time of less than 30 seconds per slice, but this will still result in 15 minutes of total scan-time when full brain coverage is needed. A further reduction in acquisition time is desirable for clinical usage, in which every minute counts. Therefore, improved reconstruction methods for MRF data are proposed, especially tailored to multi-component estimations. In in vivo scans we showed the improved image quality enabled by the proposed methods. In another study, We applied the SPIJN algorithm to MRF brain scans from MS patients. In the results that we obtained we observe that white matter changes are reflected in a component with prolonged transverse relaxation times which is less pronounced in data of healthy controls. We hypothesize that the observed component reflects an increase in extra-cellular water and allows for early characterization of white matter damage. In a related project, an adaptation on the SPIJN algorithm was introduced that is more sensitive to small local changes. The adjusted algorithm is applied to imaging data of MS patients and it is shown that it can help to identify small cerebral lesions. MRF sequences can be chosen rather freely, to further reduce the scan time and reduce the estimation error these sequences can be optimized. A method is proposed in which parameter maps of the brain are used as reference upon which the MRF flip-angle series is optimized, taking into account the used undersampling trajectories. As a result undersampling errors, a major source of estimation errors, are effectively minimized. Finally, we investigated an adjusted simulation method of MRF sequences that is able to accurately model the effects of through-plane motion, which is a major source of errors in MRF scans. Such a model may support the development of new retrospective correction methods for this type of motion as it enables proper simulation of its effects. In summary, this thesis proposes new methods for multi-component reconstruction and analysis, sequence optimization and studying the effects of motion in MRF and further investigates the possibilities of multi-component MRF.@en