In this report, we summarize our effort in developing mesoscale phase field (PF) models for predicting precipitation kinetics in alloys during thermal aging and/or under irradiation in nuclear reactors. The first part focuses on developing a method to predict the thermodynamic properties of critical nuclei, such as the sizes and concentration profiles of critical nuclei, and the nucleation barrier. These properties are crucial for quantitative simulations of precipitate evolution kinetics with PF models. An iron-chromium (Fe-Cr) alloy is chosen as a model alloy because it has valid thermodynamic and kinetic data and is an important structural material in nuclear reactors. A constrained shrinking dimer dynamics method is developed to search for the energy minimum path during nucleation. With the method, we are able to predict the concentration profiles of the critical nuclei of Cr-rich precipitates and nucleation energy barriers. Simulations show that Cr concentration distribution in the critical nucleus strongly depends on the overall Cr concentration and temperature. The Cr concentration inside the critical nucleus is much smaller than the equilibrium concentration calculated by the equilibrium phase diagram. This implies that a non-classical nucleation theory should be used to deal with the nucleation of Cr precipitates in Fe-Cr alloys. The growth kinetics of both classical and non-classical nuclei is investigated using the PF approach. A number of interesting phenomena are observed from the simulations: (1) a critical classical nucleus first shrinks toward its non-classical nucleus, then grows; (2) a non-classical nucleus has much slower growth kinetics at its earlier growth stage compared to the diffusion-controlled growth kinetics; (3) a critical classical nucleus grows faster at the earlier growth stage than the non-classical nucleus. All of these results demonstrate that it is critical to introduce the correct critical nuclei into PF modeling to correctly capture the kinetics of precipitation.