This article focuses on the relationships among material properties and material structure. It summarizes the fundamental characteristics of metals, ceramics, and polymers. The article provides information on crystal structure, atomic coordination, and crystalline defects. It discusses the relationships among microstructure and mechanical properties, and the relevance of the properties to design. The article describes the common means for increasing low-temperature strength and presents an example that shows structure-property relationships in nickel-base superalloys for high-temperature applications. The relationships of microstructure with low-temperature fracture, high-temperature fracture, and fatigue failure are also discussed.