In this chapter, we review some of the commonly observed failure modes in structures and machinery components. We are particularly interested in the science of degradation to understand the nature of progressive change in the integrity of material properties to the point that the component can no longer function in the intended manner for which it was designed. Mechanical failure does not necessarily mean fracture. Any drastic change in shape, size, or material properties that renders a component incapable of performing its intended function may be considered a failure (Collins 1993). To describe the evolution of failure, therefore, it is more appropriate to adopt the terminology of degradation or aging instead of failure.