  We give a review on entanglement purification for bipartite and multipartite
quantum states, with the main focus on theoretical work carried out by our
group in the last couple of years. We discuss entanglement purification in the
context of quantum communication, where we emphasize its close relation to
quantum error correction. Various bipartite and multipartite entanglement
purification protocols are discussed, and their performance under idealized and
realistic conditions is studied. Several applications of entanglement
purification in quantum communication and computation are presented, which
highlights the fact that entanglement purification is a fundamental tool in
quantum information processing.
