This review is devoted to the problem of critical state stability in hard superconductors and superconducting normal composites. An introduction is given to the properties of hard and composite superconductors, and to the qualitative nature of the physical processes that occur in these materials in the critical state. The dynamics of the development of instabilities of various kinds are treated in detail. Stability criteria are obtained and discussed, and theory is compared with experiment. The interaction between flux jumps and plastic strain jerks and the training phenomenon in superconductors are also covered.

DOI:https://doi.org/10.1103/RevModPhys.53.551