In the journal Nature, under the headline "Retire statistical significance", Amrhein et al. called for the concept of statistical significance to be abolished. This appeal, which was signed by about 800 other researchers, triggered a controversial discussion. One reason for the deliberately provocative call is the scientific practice in which the concept of statistical significance is often applied in an incorrect way for yes/no decisions. The criticism is not new and has been repeatedly expressed over the last 50 years. We refer to current and previously published caveats, give an overview of different applications of the concept of statistical significance as well as possible alternatives. We agree in principle with the criticism of the concept expressed by Amrhein et al. but in the absence of agreed alternatives and insufficient consideration of the many different applications of the concept of statistical significance, we consider the demand for its abolition to be exaggerated. A more pragmatic approach to the problem, supported by targeted instructions for scientists and reviewers, seems to be a more appropriate way forward.