The global transition toward sustainable energy systems underscores the strategic importance of methane (CH₄)–carbon dioxide (CO₂) mixtures in cryogenic applications. In Liquefied Natural Gas (LNG) processing and Carbon Capture, Utilization, and Storage (CCUS) networks, such mixtures are routinely exposed to low-temperature environments where phase stability becomes critical. Under these conditions, the unintended formation of solid CO₂ (dry ice) within pipelines poses significant engineering challenges, including flow blockage and potential equipment damage. Ensuring flow assurance therefore demands a rigorous understanding of the coupling between thermodynamic phase transitions and complex hydrodynamic behavior. This paper presents a comprehensive review of recent advances in gas–liquid–solid multiphase flow and phase change mechanisms in CH₄-CO₂ systems. It analyzes the thermophysical properties governing CO₂ de-sublimation and hydrate crystallization, with particular emphasis on non-equilibrium kinetics and delayed nucleation phenomena. In addition, the study assesses the capabilities of advanced modeling approaches, including Computational Fluid Dynamics (CFD), Molecular Dynamics (MD), and Machine Learning (ML) techniques, in predicting flow regime transitions and slurry transport behavior.