Superconductivity in the elements, alloys and simple compounds

•A review of superconductivity in elements, alloys and simple compounds is given.•These materials are believed to be described by BCS–Eliashberg theory.•The McMillan–Rowell inversion process is described.•Calculations of Tc’s from first principles are surveyed.•Other criteria beyond BCS to characterize these superconductors are discussed.

We give a brief review of superconductivity at ambient pressure in elements, alloys, and simple three-dimensional compounds. Historically these were the first superconducting materials studied, and based on the experimental knowledge gained from them the BCS theory of superconductivity was developed in 1957. Extended to include the effect of phonon retardation, the theory is believed to describe the subset of superconducting materials known as ‘conventional superconductors’, where superconductivity is caused by the electron–phonon interaction. These include the elements, alloys and simple compounds discussed in this article and several other classes of materials discussed in other articles in this Special Issue.