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As of now, circular economic production models of the circular economy (CEPMs), which include circular economy, bioeconomy, and circular bioeconomy, are among the main tools characterizing development policies in different countries. During the last five years, policies and strategies regarding CEPMs have promoted and contributed to the development of research on this topic. The evolution and most relevant aspects of the three CEPMs previously mentioned have been analyzed from a sample of 2190 scientific publications obtained from the Scopus database. Bibliometric analysis has been used to evaluate the approach of these models in agriculture and to introduce the ways in which they address the management of agricultural waste biomass (AWB). Results show that the circular economy is the most studied and prioritized model in China and most European countries, with the UK leading the way. Germany leads in topics related to the bioeconomy. The management policies and strategies of the circular bioeconomy are key to promoting research focused on AWB valorization since bioenergy and/or biofuel production continue to be a priority.