Diagnostic ultrasonic characterization of the heart is designed to assess the state of the myocardium with ultrasonic parameters that relate to structural or functional components of cardiac muscle. The potential cross fertilization of ideas and methods between those borne out of research in quantitative nondestructive evaluation of materials and those borne out of research in diagnostic medical applications in the area of ultrasonics represents an attractive goal. In this paper we describe our approach to tissue characterization of the heart based on quantitative ultrasonic imaging. We discuss methods of ultrasonic tissue characterization applied in laboratory and clinical investigations. Specific examples of the application of clinical quantitative tissue characterization include measurements of the hearts of patients with remote myocardial infarction, dilated cardiomyopathy, acute myocardial ischemia, and hearts of patients with diabetes. The role of anisotropy in quantitative tissue characterization and its effect on measurements obtained from specific standard echocardiographic views are reviewed.