The policy initiatives announced on both sides of the Atlantic to complement competition rules focus on two key dimensions: the contestability of markets on the one hand and fairness in their functioning on the other. The underlying idea is that the market positions of Big Tech would be inexpugnable - insofar as high barriers to entry protect them from self-regulating competition and insofar as they would have regulatory power over their respective ecosystems. Competition for the market would no longer be free, and competition in the market would be distorted. Our purpose in this working paper is to discuss these two dimensions. Are digital markets still contestable, and is the competition in them still competition on the merits? Finally, we discuss the remedies proposed to address these two alleged phenomena.