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In this review we shall describe and discuss the basics of the ion mixing phenomenon. First, the process is examined by considering only ballistic and kinematic effects associated with collisions between projectile and target atoms. We shall examine how collision cascades and the evolution of dense energy spikes affect the mixing process. We then show how material properties, such as heat of mixing and cohesive energy, influence the mixing process. These properties lead to the physical basis for the occurrence of temperature-independent and temperature-dependent mixing regimes. Finally, we shall examine the phase formation possibilities in the ion-reacted layer, and how irradiation conditions and various material properties can influence the final structure that forms.