By providing a global infrastructure for information exchange, the Internet has had a transformational impact on society at large. At the same time, a number of indicators, among them an observed ossification phenomenon, raise concerns about the ability of the Internet to support future communication needs and stipulate interest in alternative methods for internetworking. This paper considers an internetworking approach based on self-organizing application-layer networks. Rather than building a single global infrastructure that provides universal access, these networks take advantage of a diverse collection of network infrastructures to interconnect users and devices participating in a networked application. In this paper, we discuss aspects such as scalability, ability to adapt after disruptions, heterogeneous substrate networks, distributed security, and dynamically created network services. The discussions are supported by numerous measurement experiments.