Technology advancement demands energy storage devices (ESD) and systems (ESS) with better performance, longer life, higher reliability, and smarter management strategy. Designing such systems involve a trade-off among a large set of parameters, whereas advanced control strategies need to rely on the instantaneous status of many indicators. Machine learning can dramatically accelerate calculations, capture complex mechanisms to improve the prediction accuracy, and make optimized decisions based on comprehensive status information. The computational efficiency makes it applicable for real-time management. This paper reviews recent progresses in this emerging area, especially new concepts, approaches, and applications of machine learning technologies for commonly used energy storage devices (including batteries, capacitors/supercapacitors, fuel cells, other ESDs) and systems (including battery ESS, hybrid ESS, grid and microgrid-containing energy storage units, pumped-storage system, thermal ESS). The perspective on future directions is also discussed.