A solid under irradiation constitutes a nonequilibrium dynamical system, and therefore the modeling of phase stability in such systems requires a kinetic approach. This paper presents some recent advances in the atomistic modeling of precipitation under irradiation, using kinetic Monte Carlo simulations. It illustrates that vacancy-assisted and thermodynamically driven phase separation, in competition with forced atomic mixing promoted by nuclear collisions, can lead to three very different outcomes: dissolution of pre-existing precipitates, the formation of compositional patterns at the nanoscale, or macroscopic decomposition. Interstitial transport, on the other hand, when coupled with solute fl uxes, can induce the precipitation of mushy precipitates, even in ideal alloy systems. These diverse phase evolutions are shown to be rationalized by continuum modeling.