The uniform tracial ultrapower of a stably finite C*-algebra has played an important role in recent developments in regularity and classification of C*-algebras, starting with work of Matui and Sato. Scratching under the surface, one finds that the object that is really being studied is the "uniform tracial completion" of a C*-algebra - a concept that intriguingly mixes the measure-theoretic flavour of von Neumann algebras with the topological flavour of C*-algebras, and which generalize Ozawa's interesting notion of W*-bundles. I will define these objects, explain why one may want to study these objects in their own right, and touch on the wide field of open questions concerning them.