We critically synthesize research from 2014-2025 on how Earth's atmosphere, ice, and oceans work together as connected systems. Understanding these couplings is crucial for accurate assessments of how Earth's climate responds to change. The paper synthesizes major advances in modeling these interactions, including better measurements of Arctic feedback mechanisms and discoveries about ocean-ice coupling. Revolutionary observation tools, supercomputer breakthroughs, and international collaborations have improved scientists' ability to represent these coupled processes in climate models. However, significant gaps remain in understanding winter processes, ice sheet dynamics, and cross-scale interactions. The review identifies priorities for advancing coupled system modeling, including sustained observation networks and enhanced international coordination to improve Earth system predictions.