Review of machine learning tight-binding models: Route to accurate and scalable electronic simulations

The rapid advancement of machine learning based tight-binding Hamiltonian (MLTB) methods has opened new avenues for efficient and accurate electronic structure simulations, particularly in large-scale systems and long-time scenarios. This review begins with a concise overview of traditional tight-binding (TB) models, including both (semi-)empirical and first-principles approaches, establishing the foundation for understanding MLTB developments. We then present a systematic classification of existing MLTB methodologies, grouped into two major categories: direct prediction of TB Hamiltonian elements and inference of empirical parameters. A comparative analysis with other ML-based electronic structure models is also provided, highlighting the advancement of MLTB approaches. Finally, we explore the emerging MLTB application ecosystem, highlighting how the integration of MLTB models with a diverse suite of post-processing tools from linear-scaling solvers to quantum transport frameworks and molecular dynamics interfaces is essential for tackling complex scientific problems across different domains. The continued advancement of this integrated paradigm promises to accelerate materials discovery and open new frontiers in the predictive simulation of complex quantum phenomena.