Hilary Putnam (et al.) argued that the special theory of relativity shows that there can be no temporal becoming. Howard Stein replied by defining a becoming relation in Minkowski spacetime. Clifton and Hogarth extended and sharpened Stein’s results. Game over? To the contrary, it has been argued (Saunders, Callender) that the Stein-Clifton-Hogarth theorems actually support Putnam’s contention, in that if an apparently minimal condition is put on the becoming relation (the condition that two distinct events are able to “share a present”), then these theorems entail that the becoming relation must be the universal relation. I recount this dialectic in some detail and then try to define and defend a becoming relation based on a present that does indeed consist of more than one point or event but still satisfies the sort of objectivity requirements that Stein-Clifton-Hogarth require of a becoming relation. This present is not a global hyperplane or surface, however; it is a local structure. I close with some methodological (or are they metaphysical?) remarks about the relation between the present and the real and about the importance of the specious or psychological present.