During recent years, peer-to-peer (P2P) file-sharing systems have evolved in many ways to accommodate growing numbers of participating peers. In particular, new features have changed the properties of the unstructured overlay topology formed by these peers. Despite their importance, little is known about the characteristics of these topologies and their dynamics in modern file-sharing applications. This paper presents a detailed characterization of P2P overlay topologies and their dynamics, focusing on the modern Gnutella network. Using our fast and accurate P2P crawler, we capture a complete snapshot of the Gnutella network with more than one million peers in just a few minutes. Leveraging more than 18,000 recent overlay snapshots, we characterize the graph-related properties of individual overlay snapshots and overlay dynamics across hundreds of back-to-back snapshots. We show how inaccuracy in snapshots can lead to erroneous conclusions—such as a power-law degree distribution. ...