Cardiovascular magnetic resonance (MR) imaging is of proven clinical value for the noninvasive characterization of myocardial viability. Computed tomography (CT) is also being exploited for this indication. Examples of each of these imaging strategies for the assessment of myocardial viability will be provided in this review. Key MRI concepts and practical considerations such as customized MR imaging techniques and tailored imaging protocols dedicated to viability assessment are outlined with the primary focus on recent developments. Clinical applications of MR-based viability assessment are reviewed, ranging from rapid functional cine imaging to tissue characterization using T2-weighted imaging and T1-weighted late-contrast-enhanced imaging. Next, the merits and limitations of state-of-the-art CT imaging are surveyed, and their implications for viability assessment are considered. The final emphasis is on current trends and future directions in noninvasive viability assessment using MRI and CT.