Meissner effect, diamagnetism, and classical physics - a review

We review the literature on what classical physics has to say about the Meissner effect and the London equations. We first discuss the relevance of the Bohr-van Leeuwen theorem for the perfect diamagnetism of superconductors. The conclusion is that the theorem is based on assumptions that are not valid. We also point out results in the literature which prove that the magnetic flux expulsion from a sample cooled to superconductivity can be simply understood as an approach to the magnetostatic energy minimum. These results have been published several times but still many textbooks on magnetism claim that there is no classical diamagnetism, and virtually all books on superconductivity repeat Meissner's 1933 statement that flux expulsion has no classical explanation.