The leakage of carbon dioxide pipelines may result in significant incidents, such as fracture expansion, harm to humans and animals, and the loss of transported substances. Therefore, it is essential for us to accurately explain the processes of leakage and diffusion in carbon dioxide pipelines. Initially, this paper introduces the hazards of carbon dioxide leakage and the physical processes involved in such incidents. Subsequently, it systematically reviews recent research involving experiments and numerical simulations of carbon dioxide pipeline leakage at the entire process, including the in-pipe depressurization process, the near-field jetting process, and the far-field diffusion process. Moreover, it specifically discusses the differences in leakage processes between buried and overhead pipelines, highlighting the distinctive appearance resulting from leaks in buried pipelines. The Span-Wagner (SW) equation of state was found to accurately predict the thermodynamic behaviors of carbon dioxide during the entire process of pure carbon dioxide leakage and diffusion. Conversely, the GERG-2008 equation of state is better suited for carbon dioxide with impurities. Additionally, Homogenous Relaxation Model (HRM) and Delay Homogeneous Equilibrium Model (DHEM) have provided more precise predictions of carbon dioxide leakage and diffusion processes compared to the Homogeneous Equilibrium Model (HEM). The Computational Fluid Dynamics (CFD) model, in comparison to simplified models like Process Hazard Analysis Software Tool (PHAST), can better account for complex terrains, specific environmental conditions, and the impact of nearby structures or other obstacles on the carbon dioxide diffusion process. Its prediction aligns more closely with the actual results. However, research on buried carbon dioxide pipelines is still in its infancy, with only preliminary insights available at this time. Finally, this paper summarizes the research deficiencies on the leakage characteristics and diffusion laws of carbon dioxide pipelines, while providing a perspective on future research possibilities.