The S-adic conjecture claims that there exists a condition C such that a
sequence has a sub-linear complexity if and only if it is an S-adic sequence
satisfying Condition C for some finite set S of morphisms. We present an
overview of the factor complexity of S-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 Condition C".Comment: 2