Media streaming over the Internet is becoming increasingly popular. Currently, most media is delivered using global content-delivery networks, providing a scalable and robust client-server model. However, content delivery infrastructures are expensive. One approach to reduce the cost of media delivery is to use peer-to-peer (P2P) overlay networks, where nodes share responsibility for delivering the media to one another. The main challenges in P2P media streaming using overlay networks include: (i) nodes should receive the stream with respect to certain timing constraints, (ii) the overlay should adapt to the changes in the network, e.g., varying bandwidth capacity and join/failure of nodes, (iii) nodes should be intentivized to contribute and share their resources, and (iv) nodes should be able to establish connectivity to the other nodes behind NATs. In this work, we meet these requirements by presenting P2P solutions for live media streaming, as well as proposing a distributed NAT traversal solution. First of all, we introduce a distributed market model to construct an approximately minimal height multiple-tree streaming overlay for content delivery, in gradienTv. In this system, we assume all the nodes are cooperative and execute the protocol. However, in reality, there may exist some opportunistic nodes, free-riders, that take advantage of the system, without contributing to content distribution. To overcome this problem, we extend our market model in Sepidar to be effective in deterring free-riders. However, gradienTv and Sepidar are tree-based solutions, which are fragile in high churn and failure scenarios. We present a solution to this problem in GLive that provides a more robust overlay by replacing the tree structure with a mesh. We show in simulation, that the mesh-based overlay outperforms the multiple-tree overlay. Moreover, we compare the performance of all our systems with the state-of-the-art NewCoolstreaming, and observe that they provide better playback continuity and lower playback latency than that of NewCoolstreaming under a variety of experimental scenarios. Although our distributed market model can be run against a random sample of nodes, we improve its convergence time by executing it against a sample of nodes taken from the Gradient overlay. The Gradient overlay organizes nodes in a topology using a local utility value at each node, such that nodes are ordered in descending utility values away from a core of the highest utility nodes. The evaluations show that the streaming overlays converge faster when our market model works on top of the Gradient overlay. We use a gossip-based peer sampling service in our streaming systems to provide each node with a small list of live nodes. However, in the Internet, where a high percentage of nodes are behind NATs, existing gossiping protocols break down. To solve this problem, we present Gozar, a NAT-friendly gossip-based peer sampling service that: (i) provides uniform random samples in the presence of NATs, and (ii) enables direct connectivity to sampled nodes using a fully distributed NAT traversal service. We compare Gozar with the state-of-the-art NAT-friendly gossip-based peer sampling service, Nylon, and show that only Gozar supports one-hop NAT traversal, and its overhead is roughly half of Nylon’s.