In the field of energy storage, it is very important to predict the state of charge and the state of health of lithium-ion batteries. In this paper, we review the current widely used equivalent circuit and electrochemical models for battery state predictions. The review demonstrates that machine learning and deep learning approaches can be used to construct fast and accurate data-driven models for the prediction of battery performance. The details, advantages, and limitations of these approaches are presented, compared, and summarized. Finally, future key challenges and opportunities are discussed.