Scalability is a beneficial property for any kind of system. Generally, scalability ensures that the system can handle growing amounts of work in a graceful manner. In this disserta-tion, I examine the scalability of communication protocols in Peer-to-Peer (P2P) computer networks. The success of P2P file sharing applications is due to the outstanding features of this network architecture. As network participants, peers, join the system, they contribute with resources such as bandwidth, storage and processing capacity, or the content itself; moreover, the P2P architecture eliminates single points of failure. P2P can be present at various levels of network technologies, from access to backbone or provider networks, up to the P2P overlays of e...