Abstract: This review aims to comprehensively recapitulate the latest scientific advancements in methods from statistical physics, complex systems science (such as critical phenomena, network theory, percolation, critical point analysis, and entropy), and machine learning in the research and application of complex Earth systems． The integration of these methods provides new insights and perspectives for understanding the dynamics of Earth systems． By applying these methods, we can better model and analyze the interrelationships and nonlinear effects in Earth systems, revealing the system’s complexity and critical properties．