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Over the next decade, new measurements at flavour facilities will provide us with a unique opportunity to test strange, charm and bottom physics with an unprecedented level of accuracy. In this talk, I will discuss the importance of developing a corresponding set of precision calculations of flavour observables on the theoretical side, by mainly focusing on the treatment of hadronic effects in semileptonic B-decays. Given the intrinsic potential of flavour physics to be a discovery tool of particles Beyond the Standard Model (BSM), I will then discuss how flavour actually allows to investigate the properties of a specific BSM candidate: the (QCD-)axion. Data at flavour facilities are, to be more specific, absolutely crucial to put relevant constraints on the magnitude of axion couplings with matter. I will mainly focus on both flavour-universal and flavour-violating couplings of the axion with the light generations of quarks, namely up, down and strange, and I will highlight how the interplay between flavour and astroparticle physics is fundamental in order to obtain the strongest constraints on such parameters. In particular, for what concerns astrophysics, I will discuss the relevance of studies of both axion emission from core-collapse supernovae and axion absorption at neutrino-detection facilities.