The operation of nuclear power plants is challenging due to the generation of high-level radioactive waste, which presents hazards to living beings and complicates the disposal. Continuing research is underway to develop safety assessment methods for nuclear waste in deep geological repositories. Data-driven machine learning (DDML) has experienced a substantial increase in popularity in overcoming the issue of high-level radioactive waste in the nuclear industry and other fields. In this paper, we review the most recent development in DDML, with a specific focus on the current application status and research progress in nuclear waste vitrification and disposal. We discussed the commonly used supervised and unsupervised learning algorithms, including support vector machines (SVM) and clustering methods (CM), to highlight the importance of data-driven machine learning in controlling the challenges associated with radioactive waste management. Our literature survey shows that DDML significantly enhances computational ability and accuracy compared to conventional numerical methods. Data-driven machine learning improves operation efficiency and safety protocols for radioactive waste handling, leading to substantial economic benefits. It emphasizes the importance of continuous study in this domain, which can be advantageous in guiding experimental efforts and promoting ecologically public approval of nuclear activities.