Kinetic theory was developed by Maxwell (1860, 1866) and Boltzmann (1872) to give gas dynamics a solid theoretical foundation. Maxwell was the first to derive the compressible Navier-Stokes system. The resulting formulas for viscosity and thermal conductivity in terms of Newtonian microscopic dynamics was one of the earliest examples of what we now call up-scaling. Hilbert (1912) began the effort to put this theory on a firm mathematical footing. The last two decades has seen enormous progress, much of it spurred by the DiPerna-Lions theory (1989) of global solutions to the Boltzmann equation. This talk will give a history of this effort and survey some of the recent results.