First-principles studies on the intrinsic mechanical properties of various materials and systems through ab initio tensile and shear testing simulations based on density-functional theory are reviewed. For various materials, ideal tensile and shear strength and features of the deformation of bulk crystals without any defects have been examined, and the relation with the bonding nature has been analyzed. The surfaces or low-dimensional nano-structures reveal peculiar strength and deformation behavior due to local different bonding nature. For grain boundaries and metal/ceramic interfaces, tensile and shear behaviors depend on the interface bonding, which impacts on the research of real engineering materials. Remaining problems and future directions in this research field are discussed.