Augustine of Hippo declared he knew what time is until someone asked him. After 16 centuries we still largely ignore the true essence of time, but we made definite progress in studying its properties. The most striking, and somewhat intuitively (and tragically) obvious one is the irreversibility of its flow. And yet, our fundamental theories are time-reversal invariant, they do not distinguish between past and future. This is usually accounted for by assuming an immensely special initial condition of the Universe, dressed with statistical arguments. In this talk, I will show how an irreversible behaviour, and with it a growth of complexity and information, can emerge from time-reversal invariant laws, without assuming any special initial condition and without thermodynamical arguments. This phenomenon is present in General Relativity, our most advanced theory of the Universe. This irreversibility will also allow me to propose a solution of another puzzle associated with time, namely the incompatibility between the quantum and the general-relativistic notions of time.