With the ongoing miniaturization of devices and structures, thermal management has become increasingly crucial to the performance and reliability of modern electronics. As the need for improved heat dissipation and energy conversion grows, it is essential to have a sophisticated understanding of the thermal transport processes in solid-state materials including semiconductors and metals. Over the past several decades, many computational methods have emerged to study energy transport across multiple length and time scales, such as the first-principles method, molecular dynamics (MD), and Boltzmann transport equation (BTE). Although these methods have had great success in predicting thermal properties, they still face challenges that hinder the discovery of new heat transfer physics and thermally functional materials. For example, the accuracy of atomistic MD simulations is largely dependent on interatomic potentials, but empirical potentials tend to have limited accuracy due to their simple functional forms. On the other hand, while BTE is capable of describing heat carrier distributions and simulating thermal transport at the device level, the computational cost of solving BTE can be prohibitively high.Some of the challenges can be addressed through the continuous development of physical models or numerical algorithms, but this inevitably requires significant research and development efforts. As an alternative, machine learning may offer an efficient solution to these challenges by learning embedded knowledge from high-fidelity data or physical constraints. In particular, deep learning, a subset of machine learning methods, has recently achieved remarkable success in various applications. The focus of this dissertation is on atomistic MD simulations and the mesoscopic BTE method. We employ deep learning to tackle the current challenges by enhancing existing methods and creating new algorithms.In the first part of the dissertation, we develop neural network potentials (NNPs) specifically tailored for the thermal analysis of various semiconductor systems, including multiple phases of silicon, β-Ga2O3, and Si/Ge interfaces. These NNPs are trained using microscopic data and are expected to accurately reconstruct the ab initio potential energy surface. We then perform molecular dynamics simulations with these NNPs to predict thermal conductivity and phonon transport properties. Our results show good agreement between the NNP-MD predictions and experimental results, indicating the high accuracy of NNPs in describing phonon-mediated thermal transport. These NNPs also exhibit excellent transferability across different material systems. Furthermore, modal or spectral analysis can be integrated into the NNP-MD framework to determine the mode- or frequency-level contributions to the thermal transport processes.In the second part of the dissertation, we design a deep learning-based BTE solver. We develop physics-informed neural networks (PINNs) for solving the mode-resolved phonon BTE by minimizing the deviation from the governing physical laws (i.e., the phonon BTE). We perform numerical experiments (from 1D to 3D) to demonstrate the improved accuracy and efficiency of the proposed scheme in describing ballistic-to-diffusive phonon transport. Moreover, PINNs offer several advantages such as ease of implementation and fast evaluation, and their parametric learning feature enables efficient studies of conditional factors such as geometric parameters. We further extend this framework to handle large temperature gradients and to solve the coupled electron-phonon BTEs. PINNs have the potential to be a valuable tool for simulating thermal transport at the device level and may facilitate efficient inverse learning and thermal design.In general, inspired by recent advancements in machine learning, particularly deep learning, we aim to address some of the long-standing challenges in computational heat transfer using deep learning techniques. The frameworks and algorithms presented in this dissertation have the potential to provide new approaches to simulating and comprehending multi-scale thermal transport in solid-state materials.