Superconductivity on the edge of vanishing magnetic order

There should be no question that magnetism and superconductivity appear in close proximity in many if not most of the unconventional superconductors. These two phases are importantly correlated: the strongest manifestations of this superconducting pairing are generally associated with the weakest magnetism. It is often stated that this behavior results from a quantum critical point (QCP), although not all such superconductors fit into this category. In this paper we consider a second scenario for addressing these proximity phenomena in which no QCP is present. Although there are other examples for this latter category, most notable are those associated with very strongly paired superconductors that have insulating and magnetically ordered ``parent" materials. Here, too, one finds that ``failed" long range order is key to establishing superconductivity. This leads to the general question, which is the focus of this paper. Why, and how, in either of these contexts, does this proximal magnetism play a constructive role in helping to stabilize superconductivity? Our understanding here should help pave the way towards the discovery of new families of superconductors, which are expected to emerge on the brink of magnetism.