Quantitative magnetic resonance imaging for cancer is an invaluable noninvasive imaging tool with superior tissue contrast and greater specificity for disease than other imaging modalities; however, MRI is costly and lengthy, making it difficult to deploy quantitative imaging techniques alongside existing clinical protocols. Moreover, radiologists require high spatial resolution images for anatomical interpretation, which is not often reconcilable with the need for high temporal resolution in dynamic quantitative imaging schemes. The purpose of this dissertation is to develop novel analysis and acquisition methods that support fast quantitative imaging for substantiating clinical protocols without necessitating significantly longer scan times, thereby providing opportunity for clinical deployment of quantitative MRI protocols. This purpose is achieved through three distinct approaches. First, we take high temporal resolution dynamic contrast-enhanced MRI data from women with locally advanced breast cancer and retrospectively abbreviate the data to varying degrees. We subsequently analyze the full-length and abbreviated datasets with perfusion models and assess the agreement between the quantitative parameters from the full-length and abbreviated analyses, showing that scans can be shortened by up to 58%. Second, using fully sampled variable-flip angle raw data of the brain from healthy volunteers, we retrospectively accelerate the raw data by 8- to 36-fold and apply an untrained deep learning method with physics-based regularization to reconstruct the anatomical images while simultaneously computing the relevant quantitative parameter map. We achieve images with high spatial resolution and quantitative maps that agree strongly with the quantitative information computed from the fully sampled data. Finally, with the purpose of noninvasively describing tumor heterogeneity, we identify three distinct tumor habitats by clustering multiparametric quantitative information from diffusion-weighted and dynamic contrast-enhanced MRI data from a murine model of glioma collected at multiple imaging visits. We subsequently model the growth of the tumor habitats over time with a system of ordinary differential equations, thereby establishing a computationally fast pipeline for noninvasive tumor habitat growth prediction. Overall, these approaches yield novel methods that enable fast acquisition of quantitative MRI data as well as pipelines for retrospective abbreviation and analysis of existing quantitative MRI data