There is hardly any experience that seems more immediately and constantly given to us than the unrelenting flow of time and the all pervasive coming to an end of everything around and in us. Surely, the experience of change and the related deep conviction that the past is already settled and the future is not yet decided, are among the most basic and profound existential components of our life. The status of these experiences, in particular the status of what is usually called "becoming" (that is the "coming into being" of things, events or whatever term is adopted to characterize reality) have been considered by many as one of the profoundest issues of philosophy. However, while there is consensus over the fact that the "flow" or "passage" of time appears to be the most central feature of reality, when it comes to a philosophical articulation of the issue, the opinions diverge radically. The whole question of the reality of time and becoming presupposes ontological commitments from the very beginning, and the formulation of the questions is so sensitive to the initial philosophical assumptions that the whole debate has been fragmented in separate schools of thought. Physicalistic or empiricist philosophers, analytic philosophers, and phenomenologists have continued to advance their claims without taking too much into account the arguments developed outside their own camp. The analytic philosophers, in particular, sensibly disagree even among themselves. In the present essay, I shall adopt the point of view of a physicist trying to mediate among the various contenders, without thereby avoiding to take a stand on such commitments.