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The world's concern about global warming continues to rise, while CO2 sequestration is always considered as an effective measure to reduce the carbon content in the atmosphere to slow down the warming. To meet the technical requirements of this issue challenging us human beings, increasing numbers of researches have been published around this topic, among which reactive modeling is a popular viewpoint. In this paper, mathematical models governing the reactive transport process from fluid dynamics and thermal dynamics have been comprehensively reviewed, and the corresponding numerical methods have been concluded and presented in details. To help readers new in this area to have a basic knowledge of how to conduct a reactive transport modeling, some commonly used simulators are introduced in our paper, with their general simulation logic and authors' comments. Due to the urgent need of CO2 sequestration, risks are often inevitable in the practical application of CO2 injection and trapping process. Varieties of risks are concluded from different viewpoints of business, technique and social impacts, and we have presented some monitoring methods to handle these risks. It should be pointed out that long-term sequestration is still a difficulty, and the complex environmental conditions including changing temperature, porous structure, and chemical compositions are still hard to specify. Numerically speaking, high order schemes are still in need to meet the stability and convergence requirement, as well as local mass conservation property. No simulator now can handle CO2 sequestration cases in all projects, so that a more common model and solver should still be our future aim.