Abstract Liquid air energy storage (LAES) uses air as both the storage medium and working fluid, and it falls into the broad category of thermo-mechanical energy storage technologies. The LAES technology offers several advantages including high energy density and scalability, cost-competitiveness and non-geographical constraints, and hence has attracted a growing interest in recent years. As a result, several reviews have been published on the topic. However, these reviews covered little in the following aspects of LAES: dynamic simulation and optimisation, key components for LAES, LAES applications through integration, and unified economic and cost models for LAES. This article provides a comprehensive review on the LAES technology and fills the above gaps. Apart from applications in electrical grids such as peak-shaving, load shifting, and dealing with intermittency of renewable generation, the review also shows a diverse range of other LAES applications through integration, including waste heat and cold energy recovery and utilisation, multi-energy vector service provision, and sector coupling for chemical production and carbon capture. The review also leads to the recommendation of several areas for future research and development, including dynamic characteristics of whole LAES system integrated with renewables and end users; thermo-economic and dynamic optimization of stand-alone LAES and integrated systems; and experimental study on commercial systems.