This conference aims at bringing together complex and algebraic geometers from all around the world, to share recent advances pertaining to families of Kähler varieties. It will be discussed in particular of questions related to families of varieties with non-positive curvature: the study of families of hyperkähler or Calabi-Yau manifolds, of problems of degenerations of these families, or of questions revolving around the Iitaka conjecture and plurigenera… A dozen research talks by reknown experts will take place during the conference.