Several measurements of B-meson decay observables show deviations from Standard Model (SM) predictions, some of them hinting at violation of lepton flavour universality (LFU). I discusses how the anomalies in rare B decays can be explained by partial compositeness. Partial compositeness is a key ingredient of models with a composite Higgs boson and generically leads to violation of LFU. After presenting a simple model with partial compositeness that is able to explain the anomalies in rare B decays, the flavour phenomenology of a minimal UV completion of a composite Higgs model with partial compositeness is discussed: the minimal fundamental partial compositeness (MFPC) model. A virtue of the MFPC model is its capability of serving both as a solution to the naturalness problem of the SM and as an explanation of the flavour anomalies in rare B-meson decays. In view of recent new measurements, the results on which this proceedings contribution is based are updated.