In this seminar, I will first review the main features of models of fermion masses and mixing based on new symmetries of flavour. I will then introduce dark matter (DM) as a fermion singlet under the Standard Model (SM) gauge group that is however charged under the flavour symmetry. Interactions between DM and SM particles are then only mediated by the scalar fields that spontaneously break the flavour symmetry, the so-called flavons. In the case of gauged flavour symmetries, the interactions are also mediated by the new flavour gauge bosons. I will discuss the construction and the generic features of this class of models, as well as the phenomenology of an explicit example. In the second part of the seminar, I will show that solving the flavour problem of the SM with a simple U(1) flavour symmetry naturally leads to an axion that solves the strong CP problem and constitutes a viable DM candidate. In this framework, the ratio of the axion mass and its coupling to photons is related to the SM fermion masses and predicted within a small range, as a direct result of the observed hierarchies in quark and charged lepton masses. The same hierarchies determine the axion couplings to fermions, making the framework very predictive and experimentally testable by future axion and precision flavour experiments.