Climate change is one of the most urgent challenges facing the world. All countries should take joint actions to achieve the goal of carbon neutrality, which include controlling global warming to within a 1.5 °C temperature rise, to mitigate the extreme harm caused by climate change. However, ways in which to achieve economically and environmentally sustainable carbon neutrality are yet to be established. Carbon neutrality appears frequently in international policy and the scientific literature, but there is little detailed literature. It is necessary to conduct an in-depth analysis of the development context of its research. This paper analyzed the literature on carbon neutrality using bibliometric methods. A total of 1383 research papers were collected from the “Web of Science core database” from 1995 to 2021. Descriptive statistical analysis and keyword co-occurrence and literature co-citation network analyses were utilized to sort the research hotspots, and the detected bursts, the top 30 keywords in terms of word frequency, and 12 clusters were selected. It was found that the existing carbon neutrality research literature mainly focuses on carbon neutrality energy transformation, carbon neutrality technology development, carbon neutrality effect evaluation, and carbon neutrality industry examples. The analysis process involved comprehensively reading the key articles and considering the co-citation, burstiness, centrality, and other indicators under clustering; the carbon neutrality research was then divided into three stages, and evolving themes were observed. Based on the burst detection, this paper holds that with the energy structure transformation, energy consumption assessment and carbon neutrality schemes of various industries, carbon dioxide capture technology, and biogas resource utilization, urban carbon neutrality policy will become a research hotspot in the future. This paper helps to provide a reference for scholars’ theoretical research and has important reference value for policymakers to formulate relevant policy measures. It is helpful for enterprises to make strategic decisions and determine the direction of technology, for R&D and investment, and it is of considerable significance to promote the research of carbon neutrality technology.