The market power of the "Big Tech" companies - such as Google, Apple, Facebook, Amazon and Microsoft - is worrying citizens, commentators, regulators, and legislators all over the world. These companies have taken over dozens of other firms and allegedly engaged in anti-competitive practices of various sorts. We shall discuss why market forces alone are insufficient to restrain them, why competition agencies have found it difficult to investigate and discipline them, and what initiatives are being undertaken in different jurisdictions to deal with this issue.