The integration of technology in higher education is constantly evolving, and the recent emergence of generative artificial intelligence (AI), particularly AI-based chatbots, presents both opportunities and challenges. This rapid advancement raises crucial questions about the effective and appropriate implementation of these tools in learning and teaching. This study addresses this evolving landscape by investigating the who, why, and how of AI-based chatbot integration in higher education. Through a systematic review of 37 studies, informed by activity theory, we found that undergraduates are the primary users, leveraging chatbots for skill and thinking development, knowledge acquisition, and motivation enhancement. Drivers for adoption include the need for personalized learning experiences, simulation of human interaction, and the creation of safe learning environments. Currently, single, third-party, unimodal AI-based chatbots are predominantly used, primarily for academic support, writing assistance, and speaking practice, often as supplements to self-directed learning and online courses outside the traditional classroom setting. While facilitation strategies like gamification and multimodal integration aim to optimize learning, the observed positive impacts on student attitudes, motivation, and cognitive performance suggest the potential of these tools. However, inconsistencies in outcomes underscore the need for ongoing research and careful consideration by educators, administrators, and policymakers navigating this dynamic technological shift in higher education.