Inflation is now the paradigmatic theory of the Big Bang. But is it deserved? I will describe the conceptual and theoretical challenges that Inflation is still facing, argue that we should keep an open mind. In particular, I will argue that while it is a theory that claims to be a theory of initial conditions of the Universe, successful inflation actually depends on an intimate interplay between its own initial conditions and the inflationary model. I will show how one might go about probing this interplay by testing whether inflation can begin if its own initial conditions are not homogenous. ----- Follow the usual link or contact the organisers (Antoine Bourget and Edoardo Vescovi). Student introduction at 13:00.