The current status of one of the "holy grails" of nondestructive testing, the measurement of mechanical properties such as the strength, forming parameters or fracture toughness of metal polycrystals, is assessed. Starting from the perspective of materials science, the microstructural features which control various mechanical properties is reviewed, followed by a discussion, from the perspective of elastodynamics, of the degree to which these microstructural features can be sensed by ultrasonic measurements. Given this background, the possibility of achieving the "holy grail" is discussed. When the mechanical property is controlled by a single microstructural feature, the quest can be fruitful, as is illustrated by several examples. However, more generally, there will not be a one-to-one relationship between the microstructural features sensed by ultrasound and those controlling the mechanical properties, and empirical correlations which are restricted to particular situations must be utilized. It is suggested that this empiricism will be most effectively reduced if future effort is concentrated on understanding the relationships between the ultrasonic measurements and microstructural features and on developing new measurement modalities which provide complementary information.