We consider a system with the infrastructure for the creation and interconnection of large numbers of distributed persistent objects. This system is exemplified by the Internet: potentially, every appliance and document on the Internet has both persistent state and the ability to interact with large numbers of other appliances and documents on the Internet. This paper elucidates the characteristics of such a system, and proposes the compositional requirements of its corresponding infrastructure. We explore the problems of specifying, composing, reasoning about, and implementing applications in such a system. A specific concern of our research is developing the infrastructure to support structuring distributed applications by using sequential, choice, and parallel composition, in the anarchic environment where application compositions may be unforeseeable, and interactions may be unknown prior to actually occurring. The structuring concepts discussed are relevant to a wide range of distributed applications; our implementation is illustrated with collaborative Java processes interacting over the Internet, but the methodology provided can be applied independent of specific platforms.