Assessing glaciers using recent and historical data and predicting the future impacts on them due to climate change are crucial for understanding global glacier mass balance, regional water resources, and downstream hydrology. Computational methods are crucial for analyzing current conditions and forecasting glacier changes using remote sensing and other data sources. Due to the complexity and large data volumes, there is a strong demand for accelerated computing. AI-based approaches are increasingly being adopted for their efficiency and accuracy in these tasks. Thus, in the current state-of-the-art review work, available research results on the application of AI methods for glacier studies are addressed. Using selected search terms, AI-based publications are collected from research databases. They are further classified in terms of their geographical locations and glacier-related research purposes. It was found that the majority of AI-based glacier studies focused on inventorying and mapping glaciers worldwide. AI techniques like U-Net, Random forest, CNN, and DeepLab are mostly utilized in glacier mapping, demonstrating their adaptability and scalability. Other AI-based glacier studies such as glacier evolution, snow/ice differentiation, and ice dynamic modeling are reviewed and classified, Overall, AI methods are predominantly based on supervised learning and deep learning approaches, and these methods have been used almost evenly in glacier publications over the years since the beginning of this research area. Thus, the integration of AI in glacier research is advancing, promising to enhance our comprehension of glaciers amid climate change and aiding environmental conservation and resource management.