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In this paper we present an overview of experimental and modelling studies of fatigue crack growth rates in aerospace titanium alloy Ti–6Al–4V. We review work done on the subject since the 1980s to the present day, identifying test programmes and procedures and their results, as well as predictive approaches developed over this period. We then present the results of some of our recent experiments and simulations. Fatigue crack growth rates (FCGRs) under constant applied load were evaluated as a function of crack length, and the effect of overload (retardation) was considered. Crack opening was measured during cycling using digital image correlation, and residual stress intensity factor was determined using synchrotron X-ray diffraction mapping. Modelling techniques used for the prediction of FCGRs are then reviewed, and an approach based on the analysis of energy dissipation at the crack tip is proposed …