Magnetic Resonance Imaging (MRI) provides an imaging tool for non-invasive biological tissue characterization. Magnetic susceptibility is a key contrast mechanism for novel MRI techniques such as Quantitative Susceptibility Mapping (QSM). This dissertation focuses on advanced data acquisition and reconstruction methods for cardiac QSM to improve scan efficiency and to tackle challenges in cardiac and respiratory motion-compensated image reconstruction.QSM technique is based on multi-echo gradient echo (GRE) sequence for data acquisition. This thesis contributes to improvements in QSM through the following aspects: 1) a novel post-processing method is proposed using multi-echo GRE for better central vein sign visualization in multiple sclerosis lesion; 2) a non-cardiac gated single breath-hold stack-of-spirals sequence is developed for cardiac QSM, with results validated via right heart catheterization; 3) a free-breathing retrospective superior-inferior navigator based 3D spiral sequence together with an implicit neural representation learning based reconstruction framework was studied for motion-compensated cardiac QSM, and 4) cardiac QSM was applied for clinical studies including differential blood oxygen saturation and mitral annular calcification.