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Bibliometrics is an emerging thrust area of research and has become a standard tool of science policy and research management in the last decades and attracted much attention because of the substantial expansion of literature. This study aims to systematically review the worldwide productivity trends, the pattern of scientific collaboration, and research outputs of Bibliometrics research from Web of Science (WoS) web database, Science Citation Index Expanded (SCI-E). A bibliographic database of scientific papers published by authors affiliated worldwide, and containing the keywords “Bibliometric(s)” or “Scientometric(s)” or “Informetric(s)” or “Altmetric(s)” was built. A corpus of 9,630 publications was obtained and analyzed using the Histcite, VosViewer, and Biblioshiny software to highlight the evolution of the research domain. Publication rates from 2006 to 2020, organization of the research, type of documents, language-wise distribution, publication and citations trend by year, most productive countries, organizations, and authors, preferred types of sources of researchers, citations, and use of influential research; top-ranked papers, most frequently used author keywords; co-occurrence network in Bibliometrics research, Trend Topics and Topic Dendrogram, Conceptual Structure Map of each word in Bibliometrics literature, Collaboration Network (Author, Institutions and Country) were considered and quantitatively analyzed. This study contributes to the Bibliometrics research field in several ways. First, it provides the latest research status for researchers who are interested in the field through literature analysis. Second, it helps scholars become more aware of the research subfields through trend topic identification. Third, it provides insights to researchers engaging in the field and motivates attention to the relevant research.