This Element offers a review and synthesis of the theoretical analysis of mixed oligopoly, that is a hybrid market structure in which public (state-owned) and private firms interact, using a variety of strategic variables. A distinguishing feature of a mixed oligopoly is that firms have different objectives. A public firm's objective is a notion of social welfare while a private firm is profit maximising. Privatisation and partial-privatisation of a public firm is also discussed, together with several applications from diverse subfields spanning industrial organisation, applied microeconomic theory, innovation, international trade and environment policy. The authors also discuss ways in which the original analysis has been enriched to study the interaction between providers of public sector services as opposed to traditional goods.