Abstract: To systematically advance carbon peak and carbon neutrality, and adapt to climate change, the judiciary has been exploring to improve the judicial mechanism of carbon-related cases, especially in terms of case type, legal applicability and legal liabilities. However, carbon-related cases have not established a unified trial mechanism and adjudication rules. In case classification, there is no clear definition of carbon-related cases, which are often intertwined with climate change response cases. In judicial practice, some problems exist: the connection between ecological restoration responsibility and criminal punishment is not smooth; the rules applicable to "carbon sink subscription" are vague; the scope of the administrative litigation involving carbon is unclear, etc.To use judiciary to achieve carbon peak and carbon neutrality, the criteria for dividing carbon-related cases and climate change response cases should be clarified; the "criminal punishment +ecological restoration" type of legal liability should be improved; the applicable conditions for alternative restoration by "carbon sink subscription" should be regulated; and the types of carbon emission disputes that can be brought in administrative litigation should be clarified.