  Discovered almost forty years ago, inflation has become the leading paradigm
for the early universe. Originally invented to avoid the fine-tuning puzzles of
the standard model of cosmology, the so-called hot Big Bang phase, inflation
has always been the subject of intense debates. In this article, after a brief
review of the theoretical and observational status of inflation, we discuss the
criticisms that have been expressed against it and attempt to assess whether
inflation can really be viewed as a successful solution to the above mentioned
issues.
