Peer-to-Peer (P2P) live media streaming is an emerging technology that reduces the barrier to stream live events over the Internet. However, providing a high quality media stream using P2P overlay networks is challenging and gives raise to a number of issues: (i) how to guarantee quality of the service (QoS) in the presence of dynamism, (ii) how to incentivize nodes to participate in media distribution, (iii) how to avoid bottlenecks in the overlay, and (iv) how to deal with nodes that reside behind Network Address Translators gateways (NATs). In this thesis, we answer the above research questions in form of new algorithms and systems. First of all, we address problems (i) and (ii) by presenting our P2P live media streaming solutions: Sepidar, which is a multiple-tree overlay, and GLive, which is a mesh overlay. In both models, nodes with higher upload bandwidth are positioned closer to the media source. This structure reduces the playback latency and increases the playback continuity at nodes, and also incentivizes the nodes to provide more upload bandwidth. We use a reputation model to improve participating nodes in media distribution in Sepidar and GLive. In both systems, nodes audit the behaviour of their directly connected nodes by getting feedback from other nodes. Nodes who upload more of the stream get a relatively higher reputation, and proportionally higher quality streams. To construct our streaming overlay, we present a distributed market model inspired by Bertsekas auction algorithm, although our model does not rely on a central server with global knowledge. In our model, each node has only partial information about the system. Nodes acquire knowledge of the system by sampling nodes using the Gradient overlay, where it facilitates the discovery of nodes with similar upload bandwidth. We address the bottlenecks problem, problem (iii), by presenting CLive that satisﬁes real-time constraints on delay between the generation of the stream and its actual delivery to users. We resolve this problem by borrowing some resources (helpers) from the cloud, upon need. In our approach, helpers are added on demand to the overlay, to increase the amount of total available bandwidth, thus increasing the probability of receiving the video on time. As the use of cloud resources costs money, we model the problem as the minimization of the economical cost, provided that a set of constraints on QoS is satisﬁed. Finally, we solve the NAT problem, problem (iv), by presenting two NAT-aware peer sampling services (PSS): Gozar and Croupier. Traditional gossip-based PSS breaks down, where a high percentage of nodes are behind NATs. We overcome this problem in Gozar using one-hop relaying to communicate with the nodes behind NATs. Croupier similarly implements a gossip-based PSS, but without the use of relaying.