To ensure safe usage and robust performance of energy storage batteries, accurate state-of-charge (SOC) and state-of-health (SOH) estimations are required. Due to recent breakthroughs in machine learning and artificial intelligence methods, data-driven methods have attracted increased attention. This paper reports state-of-the-art research progress in machine learning-enabled methods for SOC and SOH estimations. Comprehensive comparisons are made in terms of the dataset, estimation accuracy, and battery type to provide a clear picture for SOC and SOH estimation. Moreover, the challenges and research opportunities on future SOC and SOH estimation are disclosed.