The microgrid connected with the battery energy storage system is a promising solution to address carbon emission problems and achieve the global decarbonization goal by 2050. Proper integration of the battery energy storage system in the microgrid is essential to optimize the overall efficiency as well as manage the power efficiently and securely. However, battery energy storage system integrated microgrid exhibits several concerns, including intermittencies, poor power quality, high capital cost, and energy imbalance between supply and demand. To address these shortcomings, an improved scheduling controller and optimization of the battery energy storage system are required to ensure the resilient, sustainable, and economic operation of the microgrid. Several approaches have been employed to improve the performance of microgrids; however, the review studies on controllers and optimizations based scheduling operations in microgrid have not been explored yet. In light of this research gap, this review offers a comprehensive investigation of battery energy systems scheduling operation and their impacts on decarbonization in microgrid applications. The different types of optimization objectives and constraints of the battery energy storage system are discussed, focusing on cost, capacity, lifetime, and emission. Besides, this review provides a detailed discussion and classification of the various controller and optimization methods and algorithms concerning framework, executions, key findings, benefits, research gaps, along with existing issues and challenges. Additionally, the influences of battery energy storage system scheduling controllers in the decarbonizing microgrid are analyzed rigorously. Finally, this review delivers some significant recommendations that will assist the researchers, industrialists, and policymakers in developing an advanced optimized scheduling controller of battery energy storage system towards achieving sustainable management and decarbonization goals in a microgrid.