The swift development of artificial intelligence (AI) has shifted to a new paradigm, i.e., AI agents—independent entities that can sense, think and do different things in ever-changing surroundings. This paper, through a scientometric analysis, looks at the growing territory of AI agents’ research by sifting through data related to a wide-ranging dataset of academic articles. It maps out the key research directions, the most popular areas for application, the prominent methodological approaches, and the nascent difficulties. The results reveal that there has been a considerable increase in the research related to AI agents, which is mainly due to the progress made in the field of large language models (LLMs), multimodal AI, and agentic frameworks. The most important application fields are healthcare, education, manufacturing, finance, and smart cities. The research also points to the limitations in terms of ethics, security, and operations that would need to be worked through if AI agents are to be deployed in a responsible manner. This study not only presents an organized picture of the current situation, but also indicates new areas for researchers to explore.