Social robots are becoming increasingly prominent across various domains, yet comprehensive bibliometric studies detailing the field's development are scarce. To bridge this gap, this study conducts an extensive bibliometric and network analysis of social robot research and illustrates its dynamic evolution from 1989 to 2024. Based on 5338 publications from the Scopus database, authored by 14,693 researchers, this study highlights the most prominent scholars and influential academic articles. The analysis reveals various bibliometric networks, including citation, co-citation, and collaboration networks, as well as keyword co-occurrence networks, and presents two intellectual structure maps: a conceptual structure map and a thematic map. The findings identify five distinct growth phases in social robot research, with publication output peaking in 2021. The United States, China, Italy, Japan, and the United Kingdom are the most productive and collaborative countries, and the International Journal of Social Robotics is recognized as the leading publication venue. Citation and co-citation analyses indicate that Bartneck, Belpaeme, and Scassellati are central influential authors in the field. Keyword and thematic analyses reveal four primary thematic clusters: human–robot interaction and design, assistive and healthcare applications, educational and developmental uses, and AI-driven technological advancements. These insights emphasize evolving research patterns and highlight areas with strong future growth potential, particularly in healthcare and socially assistive contexts. The key trends and influential contributions presented in the paper provide critical insights for future research and practical applications in the field of social robots.