Diverse quantitative models have been applied to analyse emission trading system, as the top effective climate change policy. This paper is the first attempt to present a comprehensive literature review on full-scale types of quantitative models in emission trading system research. The models dominating emission trading system-related literature could be categorized as optimization models, simulation models, assessment models, statistical models, artificial intelligences and ensemble models. Using different quantification and solution tools, these models complemented and enriched each other in serving the various agents involved in emission trading system and facilitating their respective emission trading system related works: the government to design emission trading system policies, enterprises to participate in emission trading system and goods markets, third parties to regulate emission trading system and emission trading system markets involving different agents. For each agent, a systematic analysis is provided on research hotspots (the challenges to address), quantitative models (to describe the problems and find the results), main findings (the policy implications from the models) and future research (potential improvements on existing models). Some interesting conclusions are obtained. (1) Generally, China was the largest contributor to emission trading system research using quantitative models (representing 35.71% of the total articles). (2) The research hotspots were decision making by enterprises under an emission trading system (20.92%), spillovers amongst emission trading system and other markets (17.54%) and allowance allocation by the government (12.52%). (3) Popular quantitative models included various optimization models (32.00%) and simulation models (29.64%). Highlights:• A variety of quantitative models have been applied to ETS research.• A comprehensive review on full-scale types of models in ETS research is presented.• Optimization, simulation, assessment, statistical, AI & ensemble models were built.• Models helpfully served the government, enterprises, third parties & market in ETS.• For each agent, hotspots, models, main findings and future research are analysed.