Résumé en anglais

In this note I present the main results about the quantitative and qualitative propagation of chaos for the Boltzmann-Kac system obtained in collaboration with C.~Mouhot in \cite{MMinvent} which gives a possible answer to some questions formulated by Kac in \cite{Kac1956}. We also present some related recent results about Kac's chaos and Kac's program obtained in \cite{MMWchaos,HaurayMischler,KleberSphere} by K.~Carrapatoso, M. Hauray, C. Mouhot, B. Wennberg and myself.