Several modelling approaches are available in the literature to predict longitudinal tensile failure of fibre-reinforced polymers. However, a systematic, blind and unbiased comparison between the predictions from the different models and against experimental data has never been performed. This paper presents a benchmarking exercise performed for three different models from the literature: (i) an analytical hierarchical scaling law for composite fibre bundles, (ii) direct numerical simulations of composite fibre bundles, and (iii) a multiscale finite-element simulation method. The results show that there are significant discrepancies between the predictions of the different modelling approaches for fibre-break density evolution, cluster formation and ultimate strength, and that each of the three models presents unique advantages over the others. Blind model predictions are also compared against detailed computed-tomography experiments, showing that our understanding of the micromechanics of longitudinal tensile failure of composites needs to be developed further.