The search for superhard materials is motivated by technical applications under extreme conditions. The term "superhard" usually denotes materials with Vickers hardness (HV) larger than 40 GPa. This chapter presents some classes of hardest compounds, and concentrates on novel nitrides and some carbides and carbonitrides. It summarizes the latest developments in modeling and synthesis as well as potential properties of advanced materials with super‐ and ultrahard mechanical properties. The chapter presents a short overview of hardness and elastic properties. The elastic properties of an isotropic homogeneous solid can be described by any two of the four quantities: Young's modulus, shear (or rigidity) modulus, bulk modulus, Poisson's ratio. The process of hardness determination involves various mechanisms, among which are volume compression, shear deformation, bond breaking, and creation and motion of dislocations. The phenomenological correlations between hardness and elastic properties of a material serve excellently to estimate hardness of a single crystal.