The recent decades have seen various attempts at the numerical modelling of fibre-reinforced polymer (FRP) composites in the aerospace, auto and marine sectors due to their excellent mechanical properties. However, it is still challenging to accurately predict the failure of the composites because of their anisotropic and inhomogeneous characteristics, multiple failure modes and their interaction, especially under multiaxial loading conditions. Micromechanics-based numerical models, such as representative volume elements (RVEs), were developed to understand the progressive failure mechanisms of composites, and assessing existing failure criteria. To this aim, this review paper summarises the development of micromechanics-based RVE modelling of unidirectional (UD) FRP composites reported in the literature, with a focus on those models developed using finite element (FE) and discrete element (DE) methods. The generation of fibre spatial distribution, constitutive models of material constituents as well as periodic boundary conditions are briefly introduced. The progressive failure mechanisms of UD FRP composites simulated by RVEs under various loadings are discussed and the comparison of failure envelopes predicted by numerical results and classical failure criteria are reviewed.