In the first part of this article, I summarise two centuries of research onturbulence. I also critically discuss some of the interpretations which are still in use,since turbulence remains an inherently non-linear problem that is still unsolved tothis day. In the second part, I tell the story of how Alex Grossmann introduced me tothe continuous wavelet representation in 1983, and how he instantly convinced methat this is the tool I was looking for to study turbulence. In the third part, I present aselection of results I obtained in collaboration with several students and colleaguesto represent, analyse and filter different turbulent flows using the continuous wavelettransform. I have chosen to present both theories and results without the use ofequations, in the hope that reading this article will be more enjoyable.