Slurry pipe transport has directed the efforts of researchers for decades, not only for the practical impact of this problem, but also for the challenges in understanding and modelling the complex phenomena involved. The increase in computer power and the diffusion of multipurpose codes based on Computational Fluid Dynamics (CFD) have opened up the opportunity to gather information on slurry pipe flows at the local level, in contrast with the traditional approaches of simplified theoretical modelling which are mainly based on a macroscopic description of the flow. This review paper discusses the potential of CFD for simulating slurry pipe flows. A comprehensive description of the modelling methods will be presented, followed by an overview of significant publications on the topic. However, the main focus will be the assessment of the potential and the challenges of the CFD approach, underlying the essential interplay between CFD simulations and experiments, discussing the main sources of uncertainty of CFD models, and evaluating existing models based on their interpretative or predictive capacity. This work aims at providing a solid ground for students, academics, and professional engineers dealing with slurry pipe transport, but it will also provide a methodological approach that goes beyond the specific application.