Peer-to-peer (P2P) computing offers new opportunities for building highly distributed data systems. Unlike client-server computing, P2P is a very dynamic environment where peers can join and leave the network at any time. This yields important advantages such as operation without central coordination, peers autonomy, and scale up to large number of peers. However, providing high-level data management services is difficult. Most techniques designed in distributed database systems which statically exploit schema and network information no longer apply. New techniques are needed which should be decentralized, dynamic and self-adaptive. In this paper, we survey the techniques which have been developed for query processing in P2P systems. We first give an overview of the existing P2P networks, and com-pare their properties from the perspective of data management. Then, we discuss the ap-proaches which are used for schema mapping. Then, we describe the algorithms which have been proposed for query routing. In particular, we focus on query routing in unstructured net-works and DHTs. Finally, we present the techniques which have been proposed for processing complex queries, e.g. top-k queries, in P2P systems, in particular in DHTs.