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Some fifty years ago, in her seminal PhD thesis, Odile Macchi introducedpermanental and determinantal point processes. Her initial motivation was toprovide models for the set of detection times in fundamental bosonic orfermionic optical experiments, respectively. After two rather quiet decades,these point processes have quickly become standard examples of point processeswith nontrivial, yet tractable, correlation structures. In particular,determinantal point processes have been since the 1990s a technical workhorsein random matrix theory and combinatorics, and a standard model for repulsivepoint patterns in machine learning and spatial statistics since the 2010s.Meanwhile, our ability to experimentally probe the correlations betweendetection events in bosonic and fermionic optics has progressed tremendously.In Part I of this survey, we provide a modern introduction to the concepts inMacchi's thesis and their physical motivation, under the combined eye ofmathematicians, physicists, and signal processers. Our objective is to providea shared basis of knowledge for later cross-disciplinary work on pointprocesses in quantum optics, and reconnect with the physical roots ofpermanental and determinantal point processes.

From point processes to quantum optics and back