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Peer-to-Peer (P2P) systems gained popularity and are responsible for a large share of today's Internet traffic. Nevertheless, their dynamic nature and the intended lack of control through central instances make their behavior unpredictable and, therefore, it is difficult to achieve a high level of Quality-of-Service for P2P traffic. Thus, peers are themselves responsible for dealing with these issues by applying so-called self-organization mechanisms to deal with their heterogeneity, unpredictable behavior, and asymmetric resources. This paper discusses and classifies relevant self-organizing aspects of P2P systems, including metrics and mechanisms. Hereby, the key focus is in better understanding on how such self-organizing mechanisms - originally designed to improve the performance of P2P overlays - affect the underlying Internet infrastructure.