Résumé
TheS -adic conjecture claims that there exists a conditionCsuch that a sequence has a sub-linear complexity if and only if it is anS -adic sequence satisfying ConditionCfor some finite setSof morphisms. We present an overview of the factor complexity ofS -adic sequences and we give some examples that either illustrate some interesting properties or that are counter-examples to what could be believed to be "a good ConditionC ".