Abstract Intensity interferometry and in particular that based on Bose–Einstein correlations (BEC) constitutes at present the only direct experimental method for the determination of sizes and lifetimes of sources in particle and nuclear physics. The measurement of these is essential for an understanding of the dynamics of strong interactions which are responsible for the existence and properties of atomic nuclei. Moreover, a new state of matter, quark matter, in which the ultimate constituents of matter move freely, is within the reach of present accelerators or those under construction. The confirmation of the existence of this new state is intimately linked with the determination of its space–time properties. Furthermore, BEC provides information about quantum coherence which lies at the basis of the phenomenon of Bose–Einstein condensation seen in many chapters of physics. Coherence and the associated classical fields are essential ingredients in modern theories of particle physics including the standard model. Last but not least besides this “applicative” aspect of BEC, this effect has implications for the foundations of quantum mechanics including the understanding of the concept of “identical particles”. Recent theoretical developments in BEC are reviewed and their application in high-energy particle and heavy-ion reactions is analysed. The treated topics include: (a) a comparison between the wave-function approach and the space–time approach based on classical currents, which predicts “surprising” particle–anti-particle BEC, (b) the study of final state interactions, (c) the use of hydrodynamics, and (d) the relation between correlations and multiplicity distributions.