The essay begins with a definition of anarchy (the anarchist Idea, the libertarian spirit) and anarchism (the anarchist thought and movement). Then, it focuses on some problematic issues of the contemporary reflection. In fact, the anarchist thought shows signs of renewal vitality, as soon as it accepts to tackle the thorny problem of the relationship within politics and democracy, that is, when it endeavors to trace the possible development of a science of anarchist politics.