Recent reports have claimed that high‐temperature superconductors can interact with gravitation under certain non‐relativistic conditions. Only two such reports have been peer‐reviewed: the first, describing changes in the weight of test masses, was by Podkletnov and Nieminen (1992); the other, reporting large‐amplitude gravitational wave generation in a laboratory, was by Podkletnov and Modanese (2003). Common to these reports is the claim that the observed gravitational field may be modified using YBa2Cu3O7−&dgr;(YBCO) below its superconducting critical temperature,Tc∼ 93K, and in a magnetic fieldB∼ 1T. Temperatures below 70K gave the largest effects. The first experiment used magnetically levitated YBCO rotated at ∼5000 rpm; the second experiment did not spin or levitate the YBCO, but used a 2MV electrical discharge in a vacuum chamber. Several attempts have been made world‐wide to replicate the first of these experiments, although no peer‐reviewed reports have yet confirmed the observations. No known replications of the second experiment have been completed so far. A number of papers have presented theoretical models for the effects. This paper reviews the current experimental and theoretical scientific evidence regarding these experiments, together with further tests implied by the published explanations. The discussion includes a classical suggestion (due to Landau and Lifshitz) that gravitational waves can modify gravitational fields, Aquino’s theory based upon electromagnetic fields, and Desbrandes’s calculation to explain the Podkletnov and Nieminen results on the basis of gravity waves emitted from the Cooper pairs inside a superconductor. The conclusions are that these experiments are extremely difficult to replicate and that no complete replication confirming the effects has yet taken place. By contrast, no‐one has conclusively disproved the existence of the effects. © 2004 American Institute of Physics