I will review some results concerning vortices in the Ginzburg-Landau model, droplets in the two-dimensional Ohta-Kawasaki model, and Coulomb gases, which all have in common that they reduce to systems of points with Coulomb interaction. I will discuss the derivation of a "renormalized energy" for the limits of such systems, and the question of crystallization. This is based on joint works with Etienne Sandier, Nicolas Rougerie, Dorian Goldman, Cyrill Muratov, Simona Rota-Nodari.