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Reactive magnetron sputtering is a well-established physical vapor technique to deposit thin compound films on different substrates, ranging from insulating glass windows over wear-resistant car parts to high-responsive touch screens. In this way, the industrial and technological relevance drives the need to understand this process on a more profound level to make optimal use of it. Notwithstanding, the basic principles of the technique can be summarized on a single sheet of paper, and truly mastering and understanding the process behavior is not a simple task. One of the main reasons is the often strong non-linear response of the reactive system to changes in the operation parameters or to small system fluctuations. This aspect of reactive sputtering is embodied by the occurrence of a hysteresis in the system observables as a function of the operation parameters. It is the existence of the hysteresis that troubles optimal deposition and process control on the one hand and gives voice to the intertwined physical and chemical complexity on the other hand. The aim of this tutorial can be considered as threefold: to acquaint the reader with an insight into the concept of the hysteresis during reactive sputtering, to touch some of the possibilities to eliminate the hysteresis, and finally, to present how to control this hysteresis in a stable operative sense. To this end, the reactive magnetron sputtering process will be formulated in practical parameters and by two discriminating phenomenological global models: the original Berg model and the reactive sputtering deposition (RSD) model. The reactive sputtering of Al in an O 2 /Ar atmosphere under direct discharge current control will be used as a reference system. The models are able to describe the hysteresis effects, giving an insight into their origin and the possibilities to eliminate them. The discharge description can, in this context, be reduced to the current/voltage or I V -characteristic and its response to a changing target state. The tutorial concludes with the existence of a double hysteresis effect and an explanation based on the RSD model. [ABSTRACT FROM AUTHOR]