  We review various contributions on the fundamental work of Lanford deriving
the Boltzmann equation from hard-sphere dynamics in the low density limit. We
focus especially on the assumptions made on the initial data and on how they
encode irreversibility. The impossibility to reverse time in the Boltzmann
equation (expressed for instance by Boltzmann's H-theorem) is related to the
lack of convergence of higher order marginals on some singular sets. Explicit
counterexamples single out the microscopic sets where the initial data should
converge in order to produce the Boltzmann dynamics.
