Fomin-Zelevinsky's cluster algebras appeared in order to
provide an algebraic framework for the study of Lusztig-Kashiwara's
canonical basis.
Since its foundation, the theory has been connected with many research
areas. One of the most fruitful link is its connection with 2 Calabi-Yau
triangulated categories. The aim of the talk is to give a survey on the
categorification of cluster algebras.