Cloud energy storage (CES) in the power systems is a novel idea for the consumers to get rid of the expensive distributed energy storages (DESs) and to move to using a cloud service centre as a virtual capacity. Although the different characteristics and applications of the energy storages are reviewed in some papers, there is no review study on the CES concepts, formulations, applications, and challenges. Therefore, the main contribution of this paper is to review the applications of the CES and its technical challenges in the power systems. For this purpose, the concept and fundamentals of the CES, as well as their role in supporting the consumers and the power network, are described first. The flow of information in a CES is then discussed, and the roles of the operator, consumers, and facilities, as the main sectors of the CES are explained. The existing studies are classified and discussed regarding the different applications of the CES in the power systems and their drawbacks are highlighted. The operation and planning (feasibility) problems of the CES are investigated. Reviewing the existing studies shows that comprehensive models are required to address the energy management (EM) and feasibility analysis of the CES applications. To address this challenge, the general formulations are presented for the planning and the operation scheduling problems of the CES. In addition, addressing different CES applications in the power systems leads to some technical challenges which are described. Finally, future directions are suggested for potential researchers to continue the studies on the CES integration and application.