In 2010, Claire Amiot conjectured that algebraic 2-Calabi-Yau
categories with cluster-tilting object must come from quivers with
potential. This would extend a structure theorem obtained with Idun
Reiten in the case where the endomorphism algebra of the cluster-tilting
object is hereditary. Many other classes of examples are also known. We
report on recent progress in the general case.