The increasing integration of renewable energy sources into power systems poses new challenges for operators. To maintain system quality and reliability, the incorporation of energy storage systems (ESSs) stands out as a promising solution. This article delves into the current and emerging trends and technologies of grid-connected ESSs. Various ESS technologies, such as mechanical, electrical, electrochemical, chemical, and thermal, are succinctly explored. A particular focus is given to battery ESSs (BESSs), given their heightened relevance amidst the ongoing electrification of transportation. Additionally, the roles that grid-connected ESSs fulfill within the grid are examined. Notably, the integration of BESSs necessitates power electronic converters, prompting a survey of popular converter topologies. These include transformer-based, transformerless (with distributed or common dc-link), and hybrid systems, alongside discussions on implementing advanced grid support functionalities in BESS control. Moreover, the article reviews the evolving standards and grid codes for grid-connected BESSs across various countries. Finally, emerging technologies like flexible power control for photovoltaic systems, hydrogen storage, and repurposing second-life batteries from electric vehicles are explored.