Individuals increasingly encounter complex challenges in areas such as mental health, physical fitness, education, and professional development, further exacerbated by rising rates of mental illnesses and chronic, lifestyle-related conditions. Coaching plays a pivotal role in fostering positive personal and professional developments, particularly by addressing the unique and complex challenges individuals face. However, access to professional coaching is often limited due to high costs, availability issues, and scalability barriers. Leveraging advancements in artificial intelligence, virtual coaches (VCs) offer tailored, autonomous coaching that addresses staff shortages and overcomes temporal and geographical constraints. However, the interdisciplinary nature of VC research - encompassing computer science, psychology, healthcare, and education - poses challenges in obtaining a comprehensive overview of existing studies. To fill this gap, we conducted a bibliometric analysis of 540 articles on VCs published between 2001 and 2024. Our analysis identifies key topics, prominent authors, leading journals, and influential institutions, providing a comprehensive mapping of the field. Based on these findings, we propose a future research agenda to further advance VC development and implementation. This study not only maps the current state of VC research but also offers valuable insights for scholars and practitioners, serving as a foundational resource for future exploration in this rapidly evolving area.