Risk assessment is a core area of climate change research. Quantitative assessment methods have been developed particularly due to the needs for theory of mitigation and adaptation strategies, and have been applied to a great number of specific assessments. However, there have been different viewpoints of the risk composition of climate change, and overall, integrated classification by coupling risk causing factors and risk bearing bodies is lacking. This article illuminates the risk composition of climate change, including the danger of risk causing factors, the exposure and vulnerability of risk bearing bodies, and their interrelations. The emergence and change of risk were clarified. Based on the integrated analysis of risk causing factors and risk bearing bodies, this study divided the climate change risk quantitative assessment methods into sudden onset hazard risk and slow onset hazard risk assessment methods, then the theoretical elaboration and case analysis were conducted for the two types of risks respectively. Finally, according to the current status and needs, this article proposes the future development directions of climate change risk research, including risk assessment under different warming amplitude, vulnerability curve construction, and adaptation.