In recent decades, nanomaterials have been at the forefront of investigations in the field of materials science, due to their beneficial size-dependent properties in many instances. The goal of this work was the development of atomistic models and new computer simulation techniques to describe phase separation in nanomaterials. The so-called Stochastic kinetic mean-field (SKMF) model has been further developed. In order to better understand the asymmetrical miscibility gap of binary systems, the gradient energy coefficient-composition function κ(c) was calculated from the interaction energy V (c) of a solution. This improved SKMF model was applied to simulate spinodal decomposition and nucleation in the Ag-Cu alloy and nanoparticles. The simulation results were compared with experimental observations of Ag-Cu nanoparticles. It was shown that the surface composition values are close to the ones calculated from a single-layer Fowler-Guggenheim approximation. I also demonstrated that this method is able to reproduce the Gibbs-Thomson effect. In addition, a new quantitative multiscale procedure based on the SKMF and phase-field models were developed to study the nucleation-growth-coarsening process in alloys.