The phenomenon of superconductivity can exist in metals, organic materials, copper oxides (cuprates), iron-pnictides, and iron-chalcogenides. The present chapter provides a brief overview of the superconducting elements, alloys, and intermetallic compounds. For the special case of MgB2, the crystal structure, the isotope effect, the presence of two superconducting energy gaps, and the effect of doping are considered. The cuprate and iron-based high-Tc superconductors are described in more detail. The crystal structures of different families of cuprate and iron-based high-Tc superconductors are presented. The phase diagrams of these complex materials and the evolution of superconductivity from Mott insulators (cuprates) or non-superconducting metals (iron-pnictides) are considered. Very recently extraordinary high critical temperatures have been observed in hydrides under extremely high pressure.