The atomistic approach of the kinetic Monte Carlo methods allows one to explicitly take into account solute atoms. In this chapter, we present and discuss the different pathways available at this point to go behind nearest neighbor pair interaction for binary alloys on rigid lattices as well as their perspectives. Different strategies to treat complex alloys with several solutes with improved cohesive models are exposed and illustrated as well as the modeling of self-interstitial diffusion under irradiation and its complexity compared to vacancy diffusion.