Battery energy storage system (BESS) is an important component of a modern power system since it allows seamless integration of renewable energy sources (RES) into the grid. A BESS is vulnerable to various cyber threats that may influence its proper operation, which in turn impacts negatively the BESS and the electric grid. The potential failure of a BESS can cause economic issues and physical damage to its components. To ensure cyber-secure and reliable BESS operation in grid-connected or islanded modes of the BESS operation, a cyber-defense strategy is needed. However, a comprehensive review on the requirements for the BESS design as well as the attack detection and mitigation methods is lacking. In this paper, we review state-of-the-art attack detection and mitigation methods for various BESS applications focusing on machine learning (ML) and artificial intelligence (AI)-based methods. In addition, the state-of-the-art methods for designing and operating a cyber-secure BESS are investigated. Based on the literature review, we identified gaps in the current research, defined the possible cyberattacks against the BESS that have not been considered before, and suggested the potential approaches to detect them.