Virtual power plants function as pivotal platforms for managing operations and facilitating transactions, significantly enhancing the visibility and collaborative operational efficiency of distributed energy resources within the main power grid. With the increasing focus on carbon reduction in the power sector, carbon trading is increasingly being integrated into virtual power plants in related research. However, a comprehensive review of carbon trading connected virtual power plants is still lacking. Therefore, this study conducts a comprehensive review and analysis of how a carbon-constrained future impacts the development and research directions of virtual power plants. An in-depth evaluation of carbon flow modeling methods employed in virtual power plants operations is provided, highlighting their respective advantages, limitations, and practical application scenarios. It analyzes how carbon transactions can be effectively integrated with the electricity market through virtual power plants and reviews the roles of virtual power plants in facilitating carbon reduction. By summarizing real-world VPPs projects, this work highlights current achievements and outlines future challenges and opportunities. It underscores the importance of developing uniform carbon accounting mechanism for market participates and electricity-carbon market coordinative scheduling method, crucial for achieving economic efficiency and social fairness in the transitioning energy sector. Additionally, further research should focus on developing new business models and advanced engagement strategies to increase consumer participation in virtual power plants.