An expanding universe is not expected to have a static vacuum energy density. The so-called cosmological constant Lambda should be an approximation, certainly a good one for a fraction of a Hubble time, but it is most likely a temporary description of a true dynamical vacuum variable that is evolving from the inflationary epoch to the present day. In this talk, I will discuss a unified picture of the cosmic history implementing such an idea. The main stages of the cosmic evolution, from inflation and its ("graceful") exit into a standard radiation regime, as well as the matter and dark energy epochs, are accounted for. We also show that for a generic Grand Unified Theory associated to the inflationary phase, the amount of entropy generated from primeval vacuum decay can explain the huge measured value today. Finally, some remarks will be made also on the implications of this picture for a possible explanation of the possible variation of the "fundamental constants".