The aim of this paper is to present the state of the art of the research on the physics of long sparks. The reference configuration is a non uniform long gap subjected to positive impulse voltages, which is the laboratory schematization of the most critical conditions occurring in the design of EHV apparatus. Under these conditions, the spark formation develops through different subsequent phases : the inception of the first ionization phenomena, the development of corona streamers, the formation of the corona stem and of the leader channel, the leader propagation, the time-evolution of the leader characteristics, the appearance of channel reilluminations, the final jump and the transition to the highly conductive spark channel. Each phase is governed by a complex interaction of electromagnetic, hydrodynamic and thermodynamic elementary processes. Each chapter of the paper presents both the experimental results and the theoretical models which have been obtained for each single phase. In recent years a number of sophisticated measuring systems have been used to study the local conditions of the different discharge phases (space charge distribution, electric field, electron energy, gas temperature and density, etc...) : the first part of each chapter presents a summary of these experimental results, in order to define the physical conditions under which the discharge develops, and to select the elementary phenomena which appear to be dominant. The second part of each chapter presents the different theoretical models, which have been obtained by simplifying the basic electromagnetic, hydrodynamic and thermodynamic equations, according to the dominant phenomena. The good agreement between computed and experimental results, over a large variety of test conditions, certify the large steps forward, which have been taken in the last years by the research on the physics of long sparks. The final objective, i.e. the formulation of a complete breakdown model, able to predict the discharge features in all the possible practical configurations, starting from the physics of the elementary phenomena, is not yet realized, but it appears as a realistic possibility of the further development of the research in this area