Abstract: Modern data centers are heavily constrained by their power budget and carbon footprint. Faced with a growing concern about the skyrocketing IT energy expenditure and the looming environmental crisis, academia and industry alike are now focusing more attention than ever on non-conventional data center power provisioning and management strategies. Recently, energy storage system (ESS) has emerged as a key enabler that allows modern data centers to greatly improve energy efficiency and system sustainability. It can help reduce data center operating expenditure (OpEx) through limiting the temporary power demand spikes caused by irregular workloads. On the other hand, it also facilitates the integration of clean and renewable energy sources (i.e. solar energy and wind energy) into the energy portfolio of green data centers. Given the growth in scale and importance of energy storage system in future data center design, this study aims to give a fairly comprehensive view of its architecture design and power management strategies. This paper surveys existing research works in two primary ESS application scenarios: power demand shaving and power supply smoothing. We compare a variety of state-of-the-art proposals and discuss major design considerations (e.g. cost, efficiency, and reliability) of ESS. We conclude today and tomorrow by discussing the opportunity and challenges created by energy storage systems in data centers.