The application of the data-driven machine learning (DDML) for the disposal of the high-level nuclear waste (HLW) is of emerging interest in the recent years. This review aims to systematically elaborate, analyze, and summarize recent advances related to DDML in the area of disposal of the HLW. Firstly, a comprehensive work on the DDML for the disposal of the HLW is examined. Five DDML algorithms including the linear regression (LR), principle component analysis (PCA) and artificial neural network (ANN) are illustrated. Then, it summarizes the typical DDML algorithms and the main inputs/outputs for the deep geological repository (DGR). Furthermore, it is concluded that the hybrid DDML algorithms are efficient choices. Also, the DDML shows a great applicability for the simulation of the multiscale and multiphysics field. Lastly, the physical-informed DDML may enhance the performance of all algorithms.