It is widely agreed that the Internet has outgrown its original architecture, and does not meet current or future needs in many areas. Most notably, requirements for network functionality, quality of service, security, and resource management are becoming too diverse for the classic IP layers. Consequently, the Internet is evolving toward a diversity of virtual networks, each with its own customized stack of layers or "overlays." This evolving architecture provides opportunities to make networked applications easier to build, deploy, and maintain. To take advantage of these opportunities, however, we need answers to many questions concerning the specification, construction, verification, and dynamic composition of overlays. This talk describes new results on overlays and architectural support for mobility. A few patterns explain the exact nature of mobility, the major implementation strategies, and how different instances of mobility can be composed and transformed. Although mobility support is only one of many Internet requirements, these preliminary results suggest that a rigorous study of overlays can lead to useful new architectural principles, as well as contribute to bridging the gap between software engineering and networking.