The use of a pneumatic conveying technique for the transportation of drill cuttings within and from offshore drill rigs is a new and challenging research field at present. In addition to experimental techniques, computational fluid dynamics (CFD) can be used for detailed understanding of the process. CFD modelling of pneumatic conveying is not very new; however, the nature of the drill cuttings introduces additional challenges for the modelling work. In the present paper, published information related to the CFD modelling of pneumatic conveying is presented in general and in detail. The information covers a wide range of pipe geometries/orientations (horizontal, vertical, different types of bends/elbows), operating conditions (air velocity, solid loading) and solid materials (particle size, particle density) being transported. The model approaches used for the predictions (Eulerian or Lagrangian, collision model, software) and the main focus/results are also presented. Next, the main challenges with regard to modelling of drill cuttings transport are addressed. The inevitable variance in cutting composition, wetness, oiliness, non-sphericity, very wide particle size distribution and degradability/instability of drill cuttings are identified as the major challenging factors. (C) 2016 Elsevier B.V. All rights reserved.