The chapter opens with Kamerlingh Onnes (1911) discovery of superconductivity in mercury at 4.2 K. It traces the study of persistent currents, specific heat and entropy, isotopic effect Meissner effect, and the failure of Ohm’s law in superconductors. A brief account of earlier theories such as two-fluid model, London equations, Ginzburg–Landau and Frohlich theory is presented but none of these could explain all aspects of superconductivity. Superconductors were classified in to two categories, type I (soft) superconductors and type II (hard) superconductors. In 1957, Bardeen, Cooper, and Schrieffer gave BCS theory which accounted for all the superconducting properties. Generalization of BCS theory by Eliashberg and McMillan equation are presented which were later used to study superconductivity in a number of elements and compounds. Discoveries of single electron quantum tunnelling and tunnelling of Cooper pairs (Josephson effect) are described which are used for measuring superconducting energy band gap. High-temperature superconductivity was discovered in 1986 by Bednorz and Müller, renewing interest in room-temperature superconductors. Theories explaining this phenomenon remain inconclusive. A brief account of experimental and theoretical developments in high temperature superconductivity is given.