Perfusion measurements in brain and liver are of high clinical interest. Arterial spin labeling (ASL) magnetic resonance imaging (MRI) has the potential to be an alternative to invasive measurements of perfusion using contrast agent-based techniques. However, the clinical application of ASL is currently limited due to a severe sensitivity to subject motion. The goal of this thesis was to develop novel methods which address the motion sensitivity of ASL sequences. The developed techniques include novel optimized approaches for background suppression, an automatic detection of breathholds during ASL experiments to suppress respiratory motion artifacts, prospective correction of respiratory motion during free-breathing scans as well as three-dimensional retrospective motion correction using a 3D GRASE PROPELLER (3DGP) readout. In addition, a novel 3DGP reconstruction, allowing joint estimation of motion and geometric distortion, is presented. Algorithms are implemented and validated in brain and liver ASL perfusion imaging using healthy volunteers. Finally, recommendations for future improvements of the developed techniques are given.