Magnetic Resonance Imaging (MRI) is a powerful noninvasive medical imaging technique capable of volumetric imaging at an arbitrary plane. Another feature of MRI is its ability to produce images with different contrasts mechanism using different image acquisition strategies; contrasts mechanisms such as proton spin relaxation (T1, T2, etc.), proton motion (diffusion, perfusion, flow, etc.), and molecular electron cloud polarization (magnetic susceptibility). This dissertation focuses on the tissue magnetic susceptibility, and the technique for the mapping of magnetic susceptibility called the Quantitative Susceptibility Mapping (QSM). Specifically, this dissertation will describe 1) the strategies for cardiac and respiratory motions compensation in QSM data acquisitions, 2) the post-processing methods for generating high quality cardiovascular magnetic susceptibility maps, 3) the initial experiences of cardiovascular QSM in clinical settings, and 4) a novel QSM reconstruction algorithm to improve the signal model in dipole inversion.