A systematic review of generative AI (GenAI) for teaching and learning in higher education (HE) was conducted, analyzing 625 research papers from Scopus, with 355 meeting inclusion criteria. The study used PRISMA guidelines and topic modelling (TM) to identify trends and themes. Key findings include the rapid growth in GenAI research since 2022, driven by the popularity of ChatGPT. The most cited journals are the Journal of Applied Learning and Teaching, the International Journal of Information Management, and the New England Journal of Medicine. Leading authors include Yogesh K. Dwivedi and Jurgen Rudolph. Co-authorship is dominated by the United States, Australia, China, and the United Kingdom. Co-occurrence analysis revealed themes such as academic integrity, ethical considerations, bias, and the integration of GenAI in education. TM identified ten core themes, including the implications of GenAI, its use in education and research, support systems, bias and inclusion, intelligent tutoring systems, machine learning applications, performance evaluation on exam questions, GenAI for writing, ethical and regulatory considerations, and deep learning models. The review highlights the potential of GenAI to enhance teaching and learning but also notes challenges such as bias, plagiarism, and ethical issues. Research gaps include the need for interdisciplinary studies, policies, and frameworks for GenAI use in HE. The study recommends further research on GenAI's impact, ethical considerations, and integration into curricula. It also emphasizes the importance of collaboration, especially in the global south, and the need for updated educational curricula to address GenAI's role in HE.A systematic review of generative AI (GenAI) for teaching and learning in higher education (HE) was conducted, analyzing 625 research papers from Scopus, with 355 meeting inclusion criteria. The study used PRISMA guidelines and topic modelling (TM) to identify trends and themes. Key findings include the rapid growth in GenAI research since 2022, driven by the popularity of ChatGPT. The most cited journals are the Journal of Applied Learning and Teaching, the International Journal of Information Management, and the New England Journal of Medicine. Leading authors include Yogesh K. Dwivedi and Jurgen Rudolph. Co-authorship is dominated by the United States, Australia, China, and the United Kingdom. Co-occurrence analysis revealed themes such as academic integrity, ethical considerations, bias, and the integration of GenAI in education. TM identified ten core themes, including the implications of GenAI, its use in education and research, support systems, bias and inclusion, intelligent tutoring systems, machine learning applications, performance evaluation on exam questions, GenAI for writing, ethical and regulatory considerations, and deep learning models. The review highlights the potential of GenAI to enhance teaching and learning but also notes challenges such as bias, plagiarism, and ethical issues. Research gaps include the need for interdisciplinary studies, policies, and frameworks for GenAI use in HE. The study recommends further research on GenAI's impact, ethical considerations, and integration into curricula. It also emphasizes the importance of collaboration, especially in the global south, and the need for updated educational curricula to address GenAI's role in HE.