A compliant carbon market is where carbon emission allowances trade takes place. The article analyzes the fundamental issues related to the carbon trading market in terms of the mechanism of carbon emission allowances allocation in the primary market, the buying and selling activities on the secondary market, and the risks in the carbon trading market. The article also analyzes and shows the difference in the adjustment method for the carbon trading market of China and the EU. Accordingly, China established a separate mechanism, its regulation only to regulate the carbon market, not recognizing it as a financial market. In contrast, the EU views carbon credits as a financial product, and therefore, regulatory regulation of carbon markets will also be subject to financial rules. Vietnam is in the process of establishing a carbon credit market. However, it has not established legal regulations related to the market establishment process without regulations governing the market operation. The research recommends that Vietnam to refer to EU regulations on considering the carbon market as a part of the financial market in order to avoid wasting the current regulatory system for the financial market.