Direct real photons are arguably the most versatile tools to study relativistic heavy ion collisions. They are produced, by various mechanisms, during the entire space-time history of the strongly interacting system. Also, being colorless, most the time they escape without further interaction, i.e. they are penetrating probes. This makes them rich in information, but hard to decypher and interpret. This review presents the experimental and theoretical developments related to direct real photons since the 1970s, with a special emphasis on the recently emerged "direct photon puzzle", the simultaneous presence of large yields and strong azimuthal asymmetries of photons in heavy ion collisions, an observation that so far eluded full and coherent explanation. CONTENTS arXiv:1907.08893v1 [nucl-ex] 21 Jul 2019 21. Hydrodynamical models 48 2. Initial state, (fast) thermalization 50 3. Transport calculations 50 4. Other ideas 52 VII. Concluding remarks 54 VIII. Acknowledgements 55 References 56 3 I. INTRODUCTIONThe centuries old quest to reveal the "ultimate" constituents of matter and the laws of Nature governing them, and the realization from quantum mechanics that mapping smaller and smaller objects requires ever larger energy probes, made high energy physics one of the dominant scientific disciplines of the XXth century. At first we took advantage of the Universe as an "accelerator" providing high energy probes (cloud chamber and emulsion experiments), but soon we started to build our own accelerators, constantly increasing their energy and luminosity. The most spectacular and best known results came in elementary particle physics, but astrophysics and nuclear physics were a close second, benefiting enormously from the progress in experimental and theoretical tools. The central question in particle physics was the substructure of hadrons and the nature of confinement, while high energy nuclear physics' foremost concern was the behavior of high density nuclear matter, including its collectivity and possible phase transition into partonic matter, which in turn evoked the early stages of the Universe. Albeit particle and nuclear physics came with different perspectives, both were concerned with the strong interaction and its underlying theory, quantum chromodynamics (QCD), so the birth of a new discipline at their intersection, relativistic heavy ion physics, was almost inevitable. From Princeton and Berkeley to Dubna the race for larger and larger ions, energies and luminosities was on. Hadrons and nuclear fragments were studied extensively, and the applicability of thermo-and hydrodynamics gradually recognized. An excellent review of these first facilities and early developments -both experimental and theoretical -can be found in [1] by Goldhaber, while a (literally) insightful account of the genesis and achievements of RHIC and LHC was given by Baym in [2].Although lepton and photon production in hadronic and nuclear collisions was studied almost since the birth of quantum mechanics and quantum electrodynamics [3][4][...