This volume deals with uniformization problems in complex geometry. These six texts corne from the six courses of the summer school « Uniformisation de familles de variétés complexes », which was held in Dijon from August 31st till September 11th, 2009 as part of ANR project Complexe ANR-08-JCJC-0130-01. From the one hand, they are written for non-specialist audience. From the other hand, they present the last developments and open problems about uniformization in various contexts. In particular, it focuses on the following topics : uniformization of foliations by curves, holomorphic geometrie structures on manifolds, Shafarevich problem about the universal cover of projective manifolds, Sullivan's dictionnary in holomorphic dynamics, foliations by complex leaves and deformation of transversely holomorphic foliations.