In recent years, machine learning, especially deep learning, has developed rapidly and has shown remarkable performance in many tasks of the smart grid field. The representation ability of machine learning algorithms is greatly improved, but with the increase of model complexity, the interpretability of machine learning algorithms is worse. The smart grid is a critical infrastructure area, so machine learning models involving it must be interpretable in order to increase user trust and improve system reliability. Unfortunately, the black-box nature of most machine learning models remains unresolved, and many decisions of intelligent systems still lack explanation. In this paper, we elaborate on the definition, motivations, properties, and classification of interpretability. In addition, we review the relevant literature addressing interpretability for smart grid applications. Finally, we discuss the future research directions of interpretable machine learning in the smart grid.