  We introduce a class of lattice gas models of active matter systems whose
hydrodynamic description can be derived exactly. We illustrate our approach by
considering two systems exhibiting two of the most studied collective
behaviours in active matter: the motility-induced phase separation and the
transition to collective motion. In both cases, we derive coupled partial
differential equation describing the dynamics of the local density and
polarization fields and show how they quantitatively predict the emerging
properties of the macroscopic lattice gases.
