Pneumatic conveying is an important operation used in many industries for the transportation of granular materials from one place to another. In recent years, many efforts have been made to study this transport process by means of the numerical approach of combing discrete element method (DEM) for particles and computational fluid dynamics (CFD) for gas. Such studies have been focused on understanding and predicting the gas-solid flow characteristics and process performance over a broad range of conditions, aiming to achieve optimal system design and control. This paper reviews the progress in this area, covering the formulation, validation and application of themathematicalmodels proposed. The emphasis is given to themodelling of key phenomena such as flow regimes and transition, pipewear, particle attrition, and electrostatics. The needs for future research are also discussed. (C) 2019 Elsevier B.V. All rights reserved.