The problem of the limits of science is twofold. First, there is the problem of demarcation, i.e., the boundaries or \"barriers\" between what is science and what is not science. Second, there is the problem of the ceiling of scientific activity, which leads to the \"confines\" of this human enterprise. These two faces of the problem of the limits -- the \"barriers\" and the \"confines\" of science -- require a new analysis, which is the task of this book. The authors take into account the Kantian roots but they are focused on the current stage of the philosophical and methodological analyses of science. This vision looks to supersede the Kantian approach in order to reach a richer conception of science.