Processing of minerals and metals involves phenomena functioning over a wide range of length scales. Equipment is generally large in order to process the required large flow rates, yet achieving the functional requirements of the operation requires successful execution of micro-scale processes. Multi-scale modelling approaches to process simulation are firstly reviewed, and similarities and differences compared with the more common multi-scale approaches to materials modelling are given. The sequential multi-scale method is then illustrated with reference to the mineral flotation process. In this case, multi-phase CFD (computational fluid dynamics) models of large-scale cells has been complemented by micro-scale CFD simulations of bubble-particle collision, and experimental and modelling studies of the bubble-particle attachment process itself. Finally, other examples of sequential multi-scale modelling are summarised, highlighting progress on unit operations including aluminium reduction cells, leaching heaps, copper solvent-extraction settlers, and fluidised beds. Crown Copyright (C) 2015 Published by Elsevier Ltd. All rights reserved.