Carbon neutrality is an important issue in addressing global environmental problems, promoting national economic development, and facilitating sustainable social development. This study used the CiteSpace software to analyze the keywords and research hotspots of 7192 English publications by international scholars and 3778 Chinese and English publications by Chinese scholars in the Web of Science and the China National Knowledge Infrastructure (CNKI) from 1991 to 2021. It revealed the current status and development trend of carbon neutrality research in China and abroad from the aspects of temporal distribution, spatial distribution, keyword co-occurrence map, and keyword clustering map. The results show that: (1) Temporally, carbon neutrality research in China and abroad can be divided into three stages: the emerging period from 1991 to 2006, the development period from 2007 to 2014, and the prosperous period from 2015 to 2021. In the twenty-first century, the number of carbon neutrality-related publications has shown a rapid growth trend, and carbon neutrality research in China showed an explosive growth in 2021, with an annual publication volume exceeding 1500. (2) Spatially, carbon neutrality research areas and research institutions have shown a trend of multi-polarization development. Countries such as the United States, China, and the United Kingdom publish a relatively large number of papers, which are mainly dominated by universities and research institutes. (3) From the perspective of research hotspots, carbon neutrality research focuses on three major scientific issues of basic research and dynamic monitoring and evaluation, technology development and application, and policy design and roadmaps. Carbon footprint, energy, carbon capture and storage technology, life cycle assessment, carbon trading market, and global governance are important research hotspots. (4) From the perspective of keyword clustering, carbon neutrality research can be clustered into four topics from the individual, industry, and country levels: individual attitude and behavior toward carbon neutrality, carbon neutrality technology, carbon market and carbon financial system, and policy guidance and global governance. This study examined the connotation and research status of each topic, and summarized the hotspots and trend of change of carbon neutrality research to provide theoretical and practical help for China to achieve the carbon neutrality goals.