Quantitative Susceptibility Mapping (QSM) is an emerging postprocessing method, computed from phase images, which is finding wide application in quantifying iron content in healthy and pathological tissue. However, QSM is still not commonly used in clinical practice. This thesis discusses the challenges that come during the application of QSM to patient studies and makes advances to solve problems such as long acquisition times, motion, and works towards finding more applications for QSM. The focus for this work is on stroke applications where methods such as Susceptibility Weighted Imaging (SWI) and Time-of-Flight (TOF) MR Angiography (MRA) are already used.SWI finds one application in the study of hemorrhage, and it has been shown in previous studies that QSM can be reconstructed from the single echo SWI sequence. However, whole brain SWI requires an acquisition time of about 5 mins which is often too long for hemorrhagic patients to remain still inside the scanner. In Chapter 2, a rapid single-shot Echo-planar Imaging (EPI) sequence with acquisition time of 0.45 mins was applied to subjects with intracerebral hemorrhage (ICH) which enabled rapid measurement of ICH area and mean magnetic susceptibility, with reduced motion as compared to standard SWI. EPI requires minimal additional acquisition time and hence can be incorporated into iron tracking studies in ICH.Motion effects cause artifacts in magnitude as well as phase images. Hence, Chapter 3 investigates the quantitative effects of movement and respiratory fluctuations on QSM in the brain. QSM was found to be more sensitive to motion caused by movement than magnitude images and thus post-processing motion correction or faster sequences may be beneficial for QSM applications. However, respiratory fluctuations did not cause statistically significant differences in susceptibility values in group study; although, these variations might be considered important in individual follow-up studies.SWI is widely used in the study of veins, hematoma, lesions etc. However, since it uses filtered phase for its computation, SWI has certain limitations such as artifacts arising from phase wraps, blooming effects, dependence of phase value on the orientation of object with main magnetic field etc. In order to overcome SWI limitations, a new method called quantitative susceptibility weighted imaging also known as true susceptibility weighted imaging (tSWI), has been recently introduced which uses susceptibility maps instead of filtered phase. Chapter 4 aims at optimizing tSWI parameters for strong susceptibility sources like hemorrhage and investigates the benefits and limitations of tSWI for hemorrhages. In hemorrhage, tSWI minimizes both blooming effects and phase wrap artifacts observed in SWI. However, unlike SWI, tSWI requires an alteration in the threshold limits for best hemorrhage depiction that greatly differs from the standard values. tSWI can be used as a complementary technique for visualizing hemorrhages along with SWI.It is always desirable to obtain maximum information from a single acquisition. Hence in Chapter 5, a new sequence has been introduced to simultaneously compute TOF-MRA, QSM, SWI and transverse relaxation rate R2* while maintaining all the key features of standard TOF-MRA such as multiple overlapping thin slab acquisition (MOTSA), ramped RF pulses and venous saturation. The effect of these TOF features on QSM and SWI was studied. The proposed sequence with the TOF features provided TOF-MRA and SWI with similar CNRs to standard methods. The mean susceptibility values for brain structures had no significant susceptibility variation between the proposed and standard methods as well. Thus, this sequence is able to provide similar TOF-MRA to standard TOF methods while enabling additions of SWI, R2* and QSM.