Pseudo Nambu-Goldstone bosons (also known as axion-like particles) with flavour-violating couplings to the Standard Model (SM) fermions are a generic consequence of spontaneously-broken global U(1) symmetries, if the SM fermions carry flavour non-universal charges. A consequence is the possible occurrence of flavour-violating decays of hadrons and leptons into light axion-like particles. These exotic signatures are a powerful probe of such kind of scenarios. A well-motivated example is the flavour-violating QCD axion arising in the context of a Froggatt-Nielsen model of fermion masses and mixing. I will discuss both the latter specific case and the more generic setup with a focus on the phenomenological consequences at future experiments, especially searches for lepton flavour violation.