Magnetic resonance imaging (MRI) has yielded great success as a medical imaging modality in the past decades, and its excellent soft tissue contrast is used in clinical routine to support diagnosis today. However, MRI is still facing challenges. For example, the acquisition time is long in comparison to computed tomography, especially when directly measuring tissue properties with quantitative MRI. This thesis presents new approaches to accelerate quantitative MRI acquisitions without decreasing the accuracy, using analytical and numerical signal models. A quantitative acquisition to map the transverse relaxation T2 was first accelerated by combining parallel imaging with model-based reconstruction. It was demonstrated that the combination leads to an improved artifact behavior in comparison to a model-based reconstruction alone, facilitating higher acceleration factors. The technique was optimized to obtain T2 maps from the brain, knee, prostate and liver, with good initial results. The idea of combining methods was continued by introducing simultaneous multi slice acquisition to the T2 mapping approach. Furthermore, a numerical simulation rather than an analytical solution was used in the model-based reconstruction, resulting in a fast undersampled acquisition that also accounts for transmit field inhomogeneity. This approach yielded more accurate and faster acquired T2 values. Magnetic resonance fingerprinting (MRF) is a recently introduced model-based reconstruction that promises to provide multiple quantitative maps using a fast pseudo-random acquisition. However, similar to other model-based approaches, MRF depends on how well the model describes the measured signal. It was demonstrated in this work that the estimated quantitative maps may be systematically biased if the model does not account for magnetization transfer effects. To this end, a simplified numerical model was proposed, that includes magnetization transfer, and yields more accurate quantitative values. The same approach was translated to bSSFP acquisitions, where banding artifacts are a major limitation: the analytical model of a phase-cycle bSSFP acquisition was used to separate signal effects of the human tissue from signal effects due to magnetic field inhomogeneity. The separation allowed the removal of typical signal voids in bSSFP images. A compressed sensing reconstruction was employed to avoid additional acquisition time. In summary, this thesis has introduced new approaches to employ signal models in different applications, with the aim of either accelerating an acquisition, or improving the accuracy of an existing fast method. These approaches may help to make the next step away from qualitative towards a fully quantitative MR imaging modality, facilitating precision medicine and personalized treatment.