In the context of climate change and energy security, the investigation of energy and carbon emission systems serves as a scientific foundation for nations to devise sustainable development strategies. Complex network models have gained significant attention in the academic community due to their ability to effectively capture intricate connections and dynamic processes. However, the applicability and interpretability of complex network modeling techniques must be fully utilized based on a deep understanding. The objective of this study is to provide a comprehensive overview of the application of complex network models within energy and carbon emission systems. To achieve this, the paper first introduces the theoretical basis. Then, the progress of complex network model application in the field of energy and carbon emissions is examined. By employing keyword co-occurrence and literature co-citation analysis, the trends and hotspots in this field are explored. Most importantly, we provided an example of renewable energy trade to illustrate the application of network modeling. This example showcases how network modeling can be applied to analyze and understand the dynamics of renewable energy trade. Lastly, the paper outlines future research directions and challenges from the perspectives of index interpretation, multi-agent modeling, and the combination of multiple methodologies. In conclusion, this research offers comprehensive insights for stakeholders interested in the application of complex network modeling in related fields.