Some Recent Results on Squarefree Words

When Axel Thue wrote these lines in the introduction to his 1912 paper on squarefree words, he certainly did not feel as a theoretical computer scientist. During the past seventy years, there was an increasing interest in squarefree words and more generally in repetitions in words. However, A. Thue's sentence seems still to hold : in some sense, he said that there is no reason to study squarefree words, excepted that it's a difficult question, and that it is of primary importance to investigate new domains. Seventy years later, these questions are no longer new, and one may ask if squarefree words served already.