Chapter 4 discusses the mechanisms and formulation of various basic particle–particle interactions. The essential modes of these interactions include a pair of spheres interacting by head-on approaching or by wake attraction, flow through a uniformly suspended sphere, electrostatic field induced by the suspended charged particles, normal collision dynamics involving forces, deformation, contact area and duration for a pair of elastic spheres, van der Waals force, and capillary force due to liquid bridge between two particles. The chapter further discusses the nonidealized particle–particle interactions and associated formulation, including the radiation transport equation for thermal radiation within a particle cloud, collision dynamics with tangential friction and torsional traction of elastic spheres, inelastic collisions, and the concept of restitution coefficient, heat and charge transfer by particle collisions, and deformation, breakup, and coalescence of fluid particles. These particle–particle interactions are critical to the model formation of dense-phase multiphase flows.