The unexpected and therefore really amazing discovery of J. G. Bednorz and K. A. R32 Miiller , that certain oxide compounds enter a superconducting state at temperatures above 30 K pushed research on superconductivity into the limelight of science in general in a way that seemed reserved for a while for high-energy or particle physics only. The common interest was then even more aroused when subsequent work rather quickly established that in the same class of compounds (oxides), critical temperatures of superconductivity above R36 the boiling point of nitrogen could be achieved . It might therefore be expected, that this entire review would solely deal with superconductivity at high temperatures, i. e. , above the boiling point of hydrogen. From my point of view, however, any unexpected occurrence of superconductivity is a challenge to scientists interested either in the physics of this phenomenon or in its materials-science aspects. In this respect, the last ten years have been quite revolutionary in the sense that on various occasions, superconductivity was discovered in materials whose physical properties were not obviously favourable for adopting this ground state. This period started with the observation that homogeneous coexistence of superconductivity and magnetic order in the same material was possible. Later it was found that electrons whose effective mass was tremendously enhanced by magnetic interactions, may also form a superconducting state, namely in materials that were subsequently identified as heavy electron superconductors.