In this essay I make a comprehensive presentation of Après la finitude by Quentin Meillassoux. The basic concepts of the book are introduced and the main lines of arguments are exposed. The focus lies on the relationship between science and philosophy, understood on the basis of a presumed conflict between on the one hand what Meillassoux calls the ancestral statements of science and on the other what he calls the correlationism of modern philosophy. Finally, I discuss the response of two prominent scholars of continental philosophy, Martin Hägglund and Catherine Malabou, to the ideas developed in Après la finitude, and thustry to assess Meillassoux’s contributionto contemporary philosophy