Log-gases and Coulomb gases are models of interacting particles who find their incarnation as eigenvalues of random matrices, as charged particles obeying the laws of electrostatics, and in the wave-function of certain quantum systems.
We present a statistical physics approach to these gases, independent of the temperature and, to a certain extent, of the dimension. We use a mixture of probabilistic and analytic tools (large deviations, transport of measures, calculus of variations, stochastic geometry) to address physical questions: definition of a free energy functional whose minimisers govern the typical behavior, description of the fluctuations, role of the temperature, universality issues. In conclusion, I will mention two longstanding open problems: the crystallization conjecture and the nature of the phase transition in the 2D Coulomb gas.