We present here a discussion of the concepts of “reversibility” and “irreversibility” of an evolution. In section 1, several reversibility concepts and the notion of an H-functional are introduced, and the relations between H-functionals and reversibility are discussed from a theoretical and, by means of examples, applied point of view. In section 2, we focus on the Boltzmann equation. After reviewing a validity result by Lanford, we suggest an explanation why the irreversibility of the equation doesn't contradict its validity. This explanation involves the weak lower semi-continuity of Boltzmann's H-functional.