As the device dimension scales down and power dissipation increases in the electronic devices, the inefficient thermal management becomes challenging for the performance and reliability. Phonons are expected to be the dominant energy carriers for the thermal transport in the nano-electronic materials such as Graphene, 2D transition metal dichalcogenides (TMDs) and β-Ga2O3. Due to the low thermal boundary conductance at the interfaces, and the scattering due to vacancy defects in these materials, the heat dissipation becomes even worse in their nano-electronic devices. A fundamental understanding of phonon transport properties of these nano-electronic materials considering the influence of interfaces, boundaries, and defects is of great importance for improving reliability and energy efficiency for the nano-electronics. In this study, we developed an atomistic framework based on the first-principle Density Functional Theory (DFT) and the Atomistic Green’s Function (AGF) to investigate the thermal transport across the vertically stacked 2-D semiconductor/substrate interfaces. The study deciphers the inherent connection among the interfacial electronic structure, charge transfer, the phonon distribution and transmission, and thermal boundary conductance at the interfaces. Furthermore, we used DFT along with the phonon Boltzmann transport equation (BTE) to study the phonon transport properties of these materials. The model for estimating the influence of boundary and vacancy defects on the thermal conductivity is developed by considering contributions of phonon boundary scattering and different types of the defect-induced phonon scattering. Our findings in this study will provide insights to engineer the interfaces for effective thermal management and future design of nano-electronics.