Aviation-induced condensation trails (contrails) and contrail cirrus represent a dominant yet uncertain component of effective radiative forcing (ERF), potentially exceeding the warming impact of accumulated carbon dioxide. As the aviation sector targets climate-optimal operations by 2030, the demand for scalable, real-time contrail forecasting has driven a fundamental paradigm shift in modeling strategies. This review provides a comprehensive analysis of contrail prediction methodologies spanning eight decades, classifying the evolution into five distinct epochs: (1) Thermodynamic and Analytical Foundations (1940s–1990s), rooted in the Schmidt-Appleman Criterion (SAC) for binary formation thresholds; (2) Microphysical Simulation (1990s–2010s), exemplified by the Contrail Cirrus Prediction (CoCiP) and APCEMM models, which resolve complex particle dynamics and lifecycle evolution; (3) NWP-Integrated Frameworks (2000s–Present), such as ECMWF IFS and WRF-Chem, which embed contrail parameterizations into global weather systems; (4) Satellite-Empirical Models, leveraging AVHRR, MODIS, and CALIOP data to establish climatological baselines and validate physical assumptions; and (5) AI-Driven and Hybrid Frontiers (2020–2026), where deep learning architectures, including U-Net segmentation, Physics-Informed Neural Networks (PINNs), and the Google-DLR hybrid system, are revolutionizing real-time detection and flight attribution. By critically evaluating the trade-offs between physical interpretability and computational scalability, this paper identifies the emerging consensus that future operational systems must adopt hybrid architectures – merging the robust constraints of first-principles physics with the adaptive precision of artificial intelligence – to enable verifiable contrail avoidance and sustainable flight planning.