Tumbling mill scale-up has had largely empirical roots. Energy size and energy size distribution relationships have been derived from relatively large data bases combined with a sprinkling of fundamental science. High fidelity simulation (HFS), which is based on multi-physics models, allows one to examine the interactions that occur in a mill amongst media, particles, wear parts and slurry at the microscale level. Thus, fundamental questions concerning particle capture, energy utilization and fragment creation as they depend on bequipment sizeQ can be addressed. In this paper, the process is taken from the single particle breakage level, through laboratory grinding experiments up to full-scale commercial mill operation. The basis for certain empirical relationships is explained in fundamental terms. A look at the future of scale-up based on the use of such tools is presented. C. 2004 Published by Elsevier B.V.