Current power systems are still highly reliant on dispatchable fossil fuels to meet variable electrical demand. As fossil fuel generation is progressively replaced with intermittent and less predictable renewable energy generation to decarbonize the power system, Electrical energy storage (EES) technologies are increasingly required to address the supply-demand balance challenge over a wide range of timescales. However, the current use of EES technologies in power systems is significantly below the estimated capacity required for power decarbonization. This paper presents a comprehensive review of EES technologies and investigates how to accelerate the uptake of EES in power systems by reviewing and discussing techno-economic requirements for EES. Individual EES technologies and power system applications are described, which provides guidance for the appraisal of specific EES technologies for specific power system services. Plausibly required scales and technology types of EES over different regions are then reviewed, followed by discussions on storage cost modelling and predictions for different EES technologies. Opportunities and challenges in developing scalable, economically viable and socio-environmental EES technologies are discussed. The paper explores EES's evolving roles and challenges in power system decarbonization and provides useful information and guidance on EES for further R&D, storage market building and policy making in the transition to zero-carbon power systems.