The popularity and bandwidth consumption attributed to current Peer-to-Peer file-sharing applications makes the operation of these distributed systems very important for the Internet community. Efficient object discovery is the first step towards the realization of distributed resource-sharing. In this work, we present a detailed overview of recent and existing search methods for unstructured Peer-to-Peer networks. We analyze the performance of the algorithms relative to various metrics, giving emphasis on the success rate, bandwidth-efficiency and adaptation to dynamic network conditions. Simulation results are used to empirically evaluate the behavior of nine representative schemes under a variety of different environments.