Agricultural straw waste and livestock manure are often misplaced resources. The separation of planting and breeding has induced significant pressure on the environment. Thus, there is a growing need for a system that can integrate crop and livestock farming to improve resource efficiency. To clarify the current state of crop–livestock systems in China and elsewhere, a bibliometric analysis was conducted for a total of 18,628 published English and 3460 published Chinese research articles and dissertations on circular agriculture. The published research papers were taken from the ISI Web of Science and CNKI database to explore research hotpots, research methods, theme trends, and mainstream technical models of crop–livestock systems from 1981 to 2021. Recent progress in crop–livestock systems was analyzed from ecological, economic, social benefits, and stakeholder perspectives. The research results showed that compared with traditional agricultural models, crop–livestock systems had far more ecologic and social benefits, including gaining higher net income and input-output ratio, improving soil quality, and mitigating global warming. The drivers of crop–livestock systems’ development were also analyzed from stakeholders’ perspectives. The study provides insights into the development of circular agriculture by reducing the pollution risks of agricultural waste and improving both ecological and economic benefits of the system.