  Inspired by recent studies of high-scale decay constant or flavorful QCD
axions, we review and clarify their existence in effective string models with
anomalous $U(1)$ gauge groups. We find that such models, when coupled to
charged scalars getting vacuum expectation values, always have one light axion,
whose mass can only come from nonperturbative effects. If the main
nonperturbative effect is from QCD, then it becomes a Peccei-Quinn axion
candidate for solving the strong CP problem. We then study simple models with
universal Green-Schwarz mechanism and only one charged scalar field: in the
minimal gaugino condensation case the axion mass is tied to the supersymmetry
breaking scale and cannot be light enough, but slightly refined models maintain
a massless axion all the way down to the QCD scale. Both kinds of models can be
extended to yield intermediate scale axion decay constants. Finally, we gauge
flavorful axion models under an anomalous $U(1)$ and discuss the axion
couplings which arise.
