Inflation is considered as the best theory of the early universe by a very large fraction of cosmologists. However, the validity of a scientific model is not decided by counting the number of its supporters, and, therefore, this dominance cannot be taken as a proof of its correctness. Throughout its history, many criticisms have been put forward against inflation. The final publication of the Planck cosmic microwave background data represents a benchmark time to study their relevance and to decide whether inflation really deserves its supremacy. In this paper, we categorize the criticisms against inflation, go through all of them in the light of what is now observationally known about the early universe, and try to infer and assess the scientific status of inflation. Although we find that important questions still remain open, we conclude that the inflationary paradigm is not in trouble but, on the contrary, has rather been strengthened by the Planck data.