How is it possible that "socialism" is today a living idea? How does it push us to a review of its complex heritage and to a research into its perspectives? What is the old and the new that socialism implies for the 21st century? After decades of neoliberal counterrevolution, the twilight of "really existing communism", the stories about the "end of history" and the (supposed) entry into a "post-political" and "post-ideological" era, it may be surprising that the questions with which we open this review continue to constitute theoretical problems of prime importance. And yet they are.