• Rigorous review on BESS sizing, constraint and optimization models are discussed. • BESS optimization objectives and methods have classified in various applications. • Explores the shortages of existing optimal BESS to identify gaps for future research. • Issues and challenges are highlighted to provide a future direction to the researchers. • Conveys significant recommendations to the researchers and policymakers. Due to urbanization and the rapid growth of population, carbon emission is increasing, which leads to climate change and global warming. With an increased level of fossil fuel burning and scarcity of fossil fuel, the power industry is moving to alternative energy resources such as photovoltaic power (PV), wind power (WP), and battery energy-storage systems (BESS), among others. BESS has some advantages over conventional energy sources, which include fast and steady response, adaptability, controllability, environmental friendliness, and geographical independence, and it is considered as a potential solution to the global warming problem. This paper provides a comprehensive review of the battery energy-storage system concerning optimal sizing objectives, the system constraint, various optimization models, and approaches along with their advantages and weakness. Furthermore, for better understanding, the optimization objectives and methods have been classified into different categories. This paper also provides a detailed discussion on the BESS applications and explores the shortages of existing optimal BESS sizing algorithms to identify the gaps for future research. The issues and challenges are also highlighted to provide a clear idea to the researchers in the field of BESS. Overall, this paper conveys some significant recommendations that would be useful to the researchers and policymakers to structure a productive, powerful, efficient, and robust battery energy-storage system toward a future with a sustainable environment.