By conducting a bibliometric analysis of 1997 scholarly publications on carbon neutrality and zero carbon emissions from 2019 to 2022, it is found that reviews of quantitative socioeconomic modeling research remain limited. To address this issue, a comprehensive review of carbon neutrality research, specifically, a systematic and synergistic review of the literature from a socioeconomic modeling perspective, is needed. The 20 clustering labels in the four largest clusters are summarized as main research streams, that is, carbon emission reduction, carbon sink and carbon capture and storage according to the definition of carbon neutral. Thus, this review revealed that carbon neutrality in the quantitative socioeconomic field is characterized in three main research directions. Sector integration, including integration within and among sectors, and integrated assessment models (IAMs), particularly multimodel analysis, can be regarded as a key node for carbon emission reduction. Carbon sink accounting, trade, and policy evaluated through technological and socioeconomic modeling, which includes both top-down and bottom-up types, are critical issues for carbon sinks. Carbon removal technologies and their application in IAMs are important topics for carbon capture and storage. This review provides a clear understanding of model-driven socioeconomic research on carbon neutrality via a systematic framework in quantitative analyses, outlining the potential gaps and challenges and providing possible insights and implications in a synergistic manner.