Numerical modelling offers the opportunity to better understand, predict, and optimise the behaviours of industrial systems, and thus provides a powerful means of improving efficiency, productivity and sustainability. However, the accurate modelling of industrial-scale particulate and particle-fluid systems is, due to the complex nature of such systems, highly challenging. This challenge arises primarily from three factors: the lack of a universally accepted continuum model for particulate media; the computational expense of discrete particle simulations; and the difficulty of imaging industrial-scale systems to obtain validation data. In recent years, however, advances in software, hardware, theoretical understanding, and imaging technology have all combined to the point where, in many cases, these challenges are now surmountable-though some distance remains to be travelled. In this review paper, we provide an overview of the most promising solutions to the issues highlighted above, discussing also the major strengths and limitations of each.