This paper introduces, describes, and compares the energy storage technologies of Compressed Air Energy Storage (CAES) and Liquid Air Energy Storage (LAES). Given the significant transformation the power industry has witnessed in the past decade, a noticeable lack of novel energy storage technologies spanning various power levels has emerged. To bridge this gap, CAES and LAES emerge as promising alternatives for diverse applications. The paper offers a succinct overview and synthesis of these two energy storage methods, outlining their core operational principles, practical implementations, crucial parameters, and potential system configurations. The article also highlights approaches to enhance the efficiency of these technologies and underscores the roles of thermal energy storage within their processes. Furthermore, it delves into the discussion of the significance of hybrid systems and polygeneration in the contexts of CAES and LAES technologies. Moreover, we briefly explore the potential integration of these technologies into other power systems.