Network virtualization and overlay networks have emerged as powerful tools for improving the flexibility of the Internet. Overlays are used to provide a wide range of useful services in today's networking environment, and they are also viewed as important building blocks for an agile and evolvable future Internet. Regardless of the specific service it provides, an overlay needs assistance in several areas in order to perform properly throughout its existence. This dissertation focuses on the mechanisms underlying the provision of auxiliary support services that perform control and management functions for overlays, such as overlay assignment, resource allocation, overlay monitoring and diagnosis. The priorities and objectives in the design of such mechanisms depend on network conditions and the virtualization environment. We identify opportunities for improvements that can help provide auxiliary services more effectively at different overlay life stages and under varying assumptions. The contributions of this dissertation are the following: 1. An overlay assignment algorithm designed to improve an overlay's diagnosability, which is defined as its property to allow accurate and low-cost fault diagnosis. The main idea is to increase meaningful sharing between overlay links in a controlled manner in order to help localize faults correctly with less effort. 2. A novel definition of bandwidth allocation fairness in the presence of multiple resource sharing overlays, and a routing optimization technique to improve fairness and the satisfaction of overlays. Evaluation analyzes the characteristics of different fair allocation algorithms, and suggests that eliminating bottlenecks via custom routing can be an effective way to improve fairness. 3. An optimization solution to minimize the total cost of monitoring an overlay by determining the optimal mix of overlay and native links to monitor, and an analysis of the effect of topological properties on monitoring cost and the composition of the optimal mix of monitored links. We call our approach multi-layer monitoring and show that it is a flexible approach producing minimal-cost solutions with low errors. 4. A study of virtual network embedding in software defined networks (SDNs), identifying the challenges and opportunities for embedding in the SDN environment, and presenting two VN embedding techniques and their evaluation. One objective is to balance the stress on substrate components, and the other is to minimize the delays between VN controllers and switches. Each technique optimizes embedding for one objective while keeping the other within bounds.