Also appears in collection : 100 (102!) Years of the Ising Model

I will survey recent and less recent aspects of the description of the scaling limit of the two-dimensional critical Ising model in terms of Conformal Loop Ensembles, which are the loop ensemble versions of the Schramm-Loewner Evolutions. In particular, we will try to illustrate the fact that many of the ideas that had emerged in the study of the discrete models appear also directly in this continuum setting that focuses on random geometric curves.