Small and medium-sized enterprises (SMEs) play a major role in economic growth in developing countries. For Vietnam, research on issues related to SMEs has grown significantly, as evidenced by increased interest and publication momentum by academic scholars. This study contributes an overview of the intellectual structure of research trends on SMEs via the Scopus database and addresses the lack of a comprehensive understanding of research patterns related to SMEs in Vietnam. This study uses a bibliometric analysis method to provide an overview of the kinds of articles, publication frequency, themes of research, etc. We found significant developments in a range of disciplines, but increased attention should be given to unsolved problems. The results reveal that the issue of innovation in SMEs has become the topic of greatest interest. Other dominant topics include knowledge management (KM), business environment issues, and issues of management in transitional economies. Business environment issues and management in transitional economies are favored by researchers, and thus we suggest that future research on Vietnamese SMEs should focus on innovation ecosystems for the entrepreneur and the characteristics and benefits of KM in developing countries such as Vietnam.