Magnetic resonance imaging (MRI) of the heart with magnetization tagging provides a potentially useful new way to assess cardiac mechanical function, through revealing the local motion of otherwise indistinguishable portions of the heart wall. While still an evolving area, tagged cardiac MRI is already able to provide novel quantitative information on cardiac function. Exploiting this potential requires developing tailored methods for both imaging and image analysis. In this paper, we review some of the progress that has been made in developing such methods for tagged cardiac MRI, as well as some of the ways these methods have been applied to the study of cardiac function.