  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.
