The literature on 'compliant' substrates is critically reviewed. Such substrates are aimed at avoiding the propagation of threading dislocations (TDs) into epitaxial layer of large misfit. The principle is to introduce a thin intermediate layer able to glide freely under the strain developed by the epitaxy. The two most successful techniques applied up to now, are the intermediate oxide layer (silicon oxide mostly) and the large angle twist-bonded layer. The origins of the 'compliance' effect are very poorly known. It is shown that the simplistic explanations generally given are totally insufficient. The very few experiments reporting detailed analysis of the various interfaces and the mechanisms are presented. A new mechanism, involving the grain boundary (GB) steps, is proposed, however, more experimental data is needed to check its validity. Experiments are suggested to improve our knowledge of the various mechanisms involved.