  We present a comprehensive discussion of the phenomenology of flavourful
axions, including both standard Peccei-Quinn (PQ) axions, associated with the
solution to the strong $CP$ problem, and non-standard axion-like particles
(ALPs). We give the flavourful axion-fermion and axion-photon couplings and
calculate the branching ratios of heavy meson ($K$, $D$, $B$) decays involving
a flavourful axion. We also calculate the mixing between axions and heavy
mesons $ K^0 $, $ D^0 $, $ B^0 $ and $ B_s^0 $, which affects the meson
oscillation probability and mass difference. Mixing also contributes to meson
decays into axions and axion decays into two photons, and may be relevant for
ALPs. We discuss charged lepton flavour-violating decays involving final state
axions of the form $\ell_1 \to \ell_2 a (\gamma) $, as well as $ \mu \to eee $
and $ \mu-e $ conversion. Finally we describe the phenomenology of a particular
"A to Z" Pati-Salam model, in which PQ symmetry arises accidentally due to
discrete flavour symmetry. Here all axion couplings are fixed by a fit to
flavour data, leading to sharp predictions and correlations between
flavour-dependent observables.
