Thirty years of the inverse problem in the calculus of variations

We consider several aspects of the inverse problem of the calculus of variations as they have developed since 1979, giving some of the principal results, listing significant primary sources and mentioning review articles for further references. The main topics involve questions of the existence and uniqueness of a Lagrangian giving rise to a given family of differential equations; we also describe some different types of inverse problem which arise in the context of quantum mechanics.