In the era of big data, the demand for data storage and processing is increasing because of advanced technologies such as artificial intelligence (AI), 5G, and cloud computing. Emerging non-volatile memory materials and devices present remarkable opportunities to enhance computing capacity. Concurrently, the AI-driven scientific research paradigm introduces a new mode for improving device performance. This review focuses on recent advances in phase-change memory materials and devices, emphasizing computational- and data-driven methodologies. Phase-change materials (PCMs) operate based on rapid and reversible phase transitions between amorphous and crystalline states, where differences in electrical and optical properties are used to encode digital information. These materials typically consist of multicomponent alloys, with phase transitions involving melting, quenching, crystallization, glass relaxation, and crystal-crystal structural changes. To achieve a detailed atomistic understanding of PCMs, large-scale density functional theory (DFT) and DFT-based ab initio molecular dynamics (AIMD) simulations are essential. Comparisons between DFT/AIMD simulations and experimental results have clarified many fundamental aspects of PCM. The first part of this review provides an overview of the history and progress in large-scale ab initio simulations of PCMs. With atomic-scale knowledge, rational materials design becomes feasible. The second part explores methods for developing new PCMs with specific properties, such as accelerating crystallization at elevated temperatures while maintaining non-volatile characteristics at room temperature. High-throughput screening's role in discovering new phase change alloys is also discussed. In the third part, we examine multiscale and cross-scale simulations of PCM for various optical and electronic phase change applications. By computing the dielectric functions of PCM during the amorphous-to-crystalline transition, we can track changes in the refractive index and extinction coefficient across visible and infrared spectra over time. These DFT-computed parameters inform coarse-grained device simulations using finite-difference time-domain (FDTD) or finite element method (FEM). Based on these multiscale simulations, we offer optimization guidelines for non-volatile color display and photonic waveguide devices. The machine learning potentials address some performance gaps between the DFT/AIMD and FEM/FDTD calculations. Machine-learning-driven molecular dynamics (MLMD) simulations serve as cross-scale simulations, with recent developments including neural networks, graph convolutional neural networks, and Gaussian approximation potentials. We discuss the role of MLMD in enabling device-scale atomistic simulations, facilitating device design and optimization with atomic-scale information. Finally, we outline future opportunities and challenges in theoretical PCM research. With ongoing AI-driven fundamental research, we anticipate the commercialization of high-performance phase change memory, neuroinspired computing, and reconfigurable nanophotonic devices, which will, in turn, foster the development of more advanced theoretical tools for research.