Mineral processing includes various processes and unit operations that involve particle flow, turbulent fluid flow, and their interactions. These multiphase systems and interactions are opaque and quite difficult to study and hence quite challenging to optimize. Empirical models suffer from an inherent drawback of not being useful beyond the range of conditions for which they are developed. This has made the use of first principle computational methods, such as discrete element modeling, computational fluid dynamics, and population balance modeling, very popular. This chapter describes the principles behind these commonly used numerical-modeling tools; Though these tools have been widely used in many mineral-processing areas, this chapter mainly gives an overview of their application in mixing, classification, grinding, and heavy media separation. © 2023 Elsevier Inc. All rights reserved.