Recent developments are summarized in the theory of Bose-Einstein and Fermi-Dirac correlations, with emphasis on the necessity of a simultaneous analysis of particle spectra and quantum statistical correlations for a detailed reconstruction of the space-time picture of particle emission. The reviewed topics are as follows: basics and formalism of quantum-statistical correlations, model-independent analysis of short-range correlations, Coulomb wavefunction corrections and the core/halo picture for n-particle Bose-Einstein correlations, the graph rules to calculate these correlations even with partial coherence in the core; particle interferometry in e + e − collisions including the Andersson-Hofmann model; the invariant Buda-Lund particle interferometry; the Buda-Lund, the Bertsch-Pratt and Yano-Koonin-Podgoretskii parameterizations, the Buda-Lund hydro model and its applications to (π/K) + p and Pb + Pb collisions at CERN SPS, and to low energy heavy ion collisions; the binary source formalism and the related oscillations in the two-particle Bose-Einstein and Fermi-Dirac correlation functions; the experimental signs of expanding rings of fire and shells of fire in particle and heavy ion physics and their similarity to planetary nebulae in stellar astronomy; the signal of partial restoration of the axial U A (1) symmetry restoration in the two-pion Bose-Einstein correlation function; the back-to-back correlations of bosons with in-medium mass modifications; and the analytic solution of the pion-laser model. Keywords: particle correlations, Bose-Einstein correlations, Fermi-Dirac correlations, quantum statistical correlations, Coulomb final-state interactions, relativistic heavy ion collisions, low and intermediate energy heavy ion collisions, hydrodynamical models, collective flow, quark-gluon plasma, hadron production by electron-positron collision PACS: 27.75. Gz, 25.75.Ld, 24.10.Hz, 12.38.Mh, 13.65.+i "Imagination is more important than knowledge."
A. Einstein