Let us consider a gas of particles undergoing the laws of ical mechanics. Depending on the physical scales in which one is interested, the gas can be described by a microscopic model (Newton's equations), a kinetic model (Boltzmann's equation...) or a hydrodynamic model (Euler, Navier-Stokes...) Hilbert's sixth problem addresses the mathematical coherence of these different descriptions. Here we shall expose some important progress achieved very recently by Bardos, Golse, Levermore, Lions, Masmoudi, Saint-Raymond, about the limit from Boltzmann's equation to various hydrodynamical incompressible equations.