Segregation control is a challenging yet crucial aspect of bulk material handling processes. The discrete element method (DEM) can offer useful insights into segregation phenomena, provided that reliable models are developed. The main challenge in this regard is finding a good balance between including particle-level details and managing the computational load. This is especially true for industrial applications, where multi-component flows consisting of particles with various irregular shapes and wide size distributions are encountered in huge amounts. In this work, we review the state of the art in DEM modelling of segregation in industrial applications involving the gravity-driven flow of dry, cohesionless granular materials. We start by introducing a novel scientific notation to distinguish between different types of mixtures. Next, we review how parameters for mixture models are determined in the current literature, and how segregation is affected by material, geometric and operational parameters based on these models. Finally, we review existing segregation indices and their applicability to multi-component segregation. We conclude that systematic calibration procedures for segregation models are currently missing in the literature, and realistic models representing multicomponent mixtures have not yet been developed. Filling these gaps will pave the way for optimising industrial processes dealing with segregation.