The question of deriving fluid mechanics equations starting from Newton's laws for the elementary particles constituting a rarefied gas, is a longstanding open problem. It was raised by Hilbert in his 6th problem in 1900. Related to this question are that of the appareance of irreversibility in Newton's (reversible) dynamics, and the so-called "propagation of chaos" introduced by Boltzmann in the late 19th century. We shall discuss both aspects of the problem, by showing how these notions appear in the derivation of the Boltzmann equation of kinetic theory (a first step towards fluid dynamics). This corresponds to a series of works in collaboration with Thierry Bodineau, Laure Saint Raymond and Sergio Simonella.