Rigid dualizing complexes

Let X be a sufficiently nice scheme. We survey some recent progress on dualizing complexes. It turns out that a complex in K(Inj=X) is dualizing if and only if tensor product with it induces an equivalence of categories from Murfet's new category K _m(Proj=X) to the category K(Inj=X). In these terms, it becomes interesting to wonder how to glue such equivalences.