The 2D two-component Coulomb gas is expected to exhibit an infinite sequence of phase transitions driven by the divergence of 2k-poles, accumulating at the Berezinskii-Kosterlitz-Thouless temperature. I will discuss joint work with Sylvia Serfaty in which we provide a rigorous proof of this "dipole transition." Our proof is based on the analysis of dipole pairs and large deviations techniques.