Magnetic susceptibility is an intrinsic tissue property that reflects underlying concentration of iron, calcification or contrast agents, which are useful for the investigation of a wide range of physiological or pathological conditions. Due to this promising outlook, there has been a long-standing interest in quantifying magnetic susceptibility. Although methods to quantify susceptibility of certain material samples have been proposed in the past, a practical means to measure an arbitrary susceptibility distribution in a living organism was lacking. Consequently, many of the potential applications were still in speculation. This thesis reports a framework that allows quantitative mapping of magnetic susceptibility in human brain using magnetic resonance imaging (MRI). Two major building blocks were proposed to overcome the technical hurdles. First, a background field removal method was developed to obtain the magnetic field of interest free of contamination from background sources. Second, two independent methods were proposed to solve a classical ill-posed inverse problem of determining susceptibility sources from measured magnetic field. With these technical developments, quantitative susceptibility mapping was realized. Its utility was demonstrated in a molecular MRI application, where identification and quantification of iron-based contrast agents are now feasible, and in cerebral MRI, where susceptibility provides a more objective measurement of hemorrhage, allowing cross-center comparisons and longitudinal studies.