The development of a consistent picture for the processes of decoherence and quantum measurement requires a treatment which is compatible with the theory of relativity. This volume reviews some of the approaches suggested to solve or circumvent the arising difficulties. Starting from an analysis of the level of compatibility of the measurement problem with the special theory of relativity, the role of non-locality and entanglement are discussed. The subject is also addressed from the point of view of quantum optics and quantum information theory, as well as on the basis of group theoretic and algebraic methods. The emergence of decoherence in quantum electrodynamics is discussed from an open systems perspective.