A method for energy storage and recovery is based on the liquid air energy storage (LAES) operated at the pressure relationship such that the pressure of discharge air is greater than the charge air to provide a high round-trip efficiency. External cold source and cold thermal energy storage are used in a LAES to achieve a decrease in the LAES capital costs. A demand for a supplemental cold energy provided by external sources may be minimized. These features alone or in combination may result in reduced power demand required for cooling.