Chapter 3 provides basic formulation of various fluid–particle interactions of an isolated object that has a relative motion in a fluid flow and in the absence of any interactions with other transported objects in the same fluid flow. The chapter describes the distinctly different transport mechanisms governing the fluid–particle interactions, their basic mathematical formula, and the corresponding ranges of validation. The most essential interactions are represented by the drag force, carried mass, Basset force, Saffman force, Magnus force, Stefan flux, and d2-law of diffusive evaporation. The most essential formulation of these fluid–particle interactions is derived with the Newtonian fluid flowing over a rigid sphere and under the creeping flow conditions. This approximated method leads to the basic formulation of the Lagrangian modeling approach for the discrete phase transport in a multiphase flow. Application of the fluid–particle interactions for the transport of isolated objects in a carrying fluid flow are illustrated.The usefulness of the order-of-magnitude analysis of the transport mechanisms in modeling simplification also is discussed.