We use Gaia Data Release 2 to determine the mean proper motions for 150 Milky Way globular clusters (almost the entire known population), with a typical uncertainty of 0.05mas/yr limited mainly by systematic errors. Combining them with distance and line-of-sight velocity measurements from the literature, we analyse the distribution of globular clusters in the 6D phase space, using both position/velocity and action/angle coordinates. The population of clusters in the central 10kpc has a mean rotational velocity reaching 50-80km/s, and a nearly isotropic velocity dispersion 100-120km/s, while in the outer galaxy, the cluster orbits are strongly radially anisotropic. We confirm a concentration of clusters at high radial action in the outer region of the Galaxy. Finally, we explore a range of equilibrium distribution function-based models for the entire globular cluster system, and the information they provide about the potential of the Milky Way. The dynamics of clusters is best described by models with the circular velocity between 10 and 50kpc staying in the range 210-240km/s.