In this conference, aimed to non-specialists of the field, I will describe the latest knowledges concerning the physics in play in the Early Universe. I will concentrate in particular to the mechanisms of transfer of energy from an inflationary state (dominated by a scalar condensate) to a matter state and then a Universe dominated by radiation, dark matter and then dark energy. These phase transitions have characteristics with some signatures that could be observed in the Cosmological Microwave Background (CMB). I will insist on the gravitational production of quanta, which lies to the frontier of a quantum theory of gravity.