In this conference, I start by presenting the first applications and developments of wavelet methods made in Marseille in 1985 in the framework of sounds and music. A description of the earliest wavelet transform implementation using the SYTER processor is given followed by a discussion related to the first signal analysis investigations. Sound examples of the initial sound transformations obtained by altering the wavelet representation are further presented. Then methods aiming at estimating sound synthesis parameters such as amplitude and frequency modulation laws are described. Finally, new challenges brought by these early works are presented, focusing on the relationship between low-level synthesis parameters and sound perception and cognition. An example of the use of the wavelet transforms to estimate sound invariants related to the evocation of the "object" and the "action" is presented.