Thue, Combinatorics on words, and conjectures inspired by the Thue-Morse sequence

Nous d'ecrivons quelques r'esultats r'ecents sur la suite de Thue-Morse, ainsi que des questions ou conjectures, dont l’une, due `a Shevelev, est r'esolue dans cet article. We describe some recent results on the Thue-Morse sequence. We also list open questions and conjectures, one of which is due to Shevelev and proved in this paper.