The advent of generative artificial intelligence (GAI) has resulted in significant transformations across diverse sectors, with higher education being a notable beneficiary. The integration of GAI into higher education marks a paradigm shift in the methodologies employed by educational institutions for teaching and learning. This review commences by furnishing a definition of the GAI and introducing its fundamental and core technologies. It then proceeds to comprehensively encapsulate the prevalent applications of GAI within higher education, zeroing seven pivotal aspects: personalized learning experiences, automated content generation, virtual teaching assistants, enhancing academic communication, assessment and feedback mechanisms, data analytics, and faculty support and development. Additionally, this review delves into the ethical dilemmas posed by the GAI era, highlighting academic integrity, data privacy and security, algorithmic bias and fairness, and transparency and accountability. Ultimately, this review concludes by suggesting several invaluable research avenues for other researchers to consider and draw inspiration from.