||In this talk, I will introduce random normal matrix models, interpreted as 2D determinantal Coulomb gases, and present macroscopic and microscopic properties of the model. A recent work on a random normal matrix model with a soft edge will be discussed. This model interpolates the hard edge case, the free boundary case, and the weakly confining case. I will describe the universality of the local eigenvalue statistics at a soft edge of the spectrum for the case when the external potential is radially symmetric. This talk is based on joint work with Nam-Gyu Kang and Yacin Ameur.