Lanthanide phosphates (
LnPO
4
) are considered as a potential nuclear waste form for immobilization of Pu and minor actinides (Np, Am, and Cm). In that respect, in the recent years we have applied advanced atomistic simulation methods to investigate various properties of these materials on the atomic scale. In particular, we computed several structural, thermochemical, thermodynamic and radiation damage related parameters. From a theoretical point of view, these materials turn out to be excellent systems for testing quantum mechanics-based computational methods for strongly correlated electronic systems. On the other hand, by conducting joint atomistic modeling and experimental research, we have been able to obtain enhanced understanding of the properties of lanthanide phosphates. Here we discuss joint initiatives directed at understanding the thermodynamically driven long-term performance of these materials, including long-term stability of solid solutions with actinides and studies of structural incorporation of
f
elements into these materials. In particular, we discuss the maximum load of Pu into the lanthanide-phosphate monazites. We also address the importance of our results for applications of lanthanide-phosphates beyond nuclear waste applications, in particular the monazite-xenotime systems in geothermometry. For this we have derived a state-of-the-art model of monazite-xenotime solubilities. Last but not least, we discuss the advantage of usage of atomistic simulations and the modern computational facilities for understanding of behavior of nuclear waste-related materials.