This thesis studies the applications of mould techniques to Kashiwara-Vergne theory. Developed by Jean Ecalle, originally to the purpose of resurgence theory, mould theory proved to be particularly well suited to the study of Multiple Zeta Values. The conjectural isomorphism between the double shuffle and Kashiwara-Vergne Lie algebras naturally led to the transfer of mould techniques from one space to the other. The first chapter is dedicated to presenting the three main spaces: the double shuffle Lie algebra from number theory, the Grothendieck-Teichmüller Lie algebra related to topology and the Kashiwara-Vergne Lie algebra from Lie theory. The second chapter introduces mould theory, using examples linked to the Lie algebras above. It then explains how to translate the defining properties of these spaces into moulds. The third and last chapter is dedicated to the elliptic versions of the Kashiwara-Vergne Lie algebra and contains the main results of this thesis.