Antitrust agencies all over the world have been investigating large digital platforms for practices which may constitute an abuse of dominance. Here I discuss practices (including ‘self-preferencing’ and denial or degradation of interoperability) which can be interpreted as foreclosure in vertically-related or complementary markets. I discuss, in particular, a few high-profile cases involving Amazon, Apple, Facebook and Google. I focus on possible theories of harm for such cases and show that both original simple models and well-established economic theories (adapted or interpreted) provide a rationale for anti-competitive foreclosure.