This book aims to develop a philosophical theory of extrinsic properties of properties whose instantiation by an object does not only depend on what the object itself is like, but also on features of its environment. Various accounts of the intrinsic/extrinsic distinction are analysed in detail, and it is argued that the most promising approach to defining this distinction is to consider extrinsic properties as a particular type of relational property. Moreover, it is shown that two key notions in the metaphysics of properties, the supervenience relation and the dispositional/categorical distinction, whose scope is usually restricted to intrinsic properties, can fruitfully be applied to extrinsic properties as well.