The continuously growing population and urban growth rates are responsible for the sharp rise in energy consumption, which leads to increased CO2 emissions and demand-supply imbalances. The power sector is switching to alternative energy sources, including renewable energy resources (RES) such as Photovoltaic (PV) and wind power (WP) and battery energy storage systems (BESS), among others, due to an increase in the use of fossil fuels and their shortage. Since the power generation of these resources is uncertain due to climatic fluctuations and the direct integration of these resources into the power grid is very complex due to the issues such as; voltage and frequency regulation, overloading of active transmission lines, and supply-demand disparity, the research on system uncertainties is receiving increasing attention. This study provides a comprehensive analysis of the several parameters of uncertainty, approaches for dealing with the uncertainty in battery energy storage (BES)-based RES integrated grid, and the advantages and disadvantages of each method. Moreover, various analytical and numerical approaches were developed for integrating RES and BESS into the power grid, including probabilistic methods, possibilistic methods, robust optimization-based techniques, and machine learning algorithms. The comparative analysis of these approaches highlights their relative strengths and weaknesses, providing a valuable resource for researchers and utility planners. Additionally, this review paper identifies several issues and challenges associated with the integration of RES and BESS into the power grid, such as power quality, economical effect, battery aging effect, and environmental effect. Furthermore, the paper suggests a few future research directions, including the development of novel models for analyzing uncertainty in power systems, coordination of uncertainty parameters, integration of BESS into RES and grid, power electronics integration, and environmental factor. Overall, this article's novel contributions include a comprehensive analysis of uncertainty parameters, a comparative analysis of uncertainty modeling approaches, an identification of critical issues and challenges, and the suggestion of future research directions to promote a sustainable and reliable power system. This article will aid in defining the requirements and specifications for novel models for analyzing uncertainty in power systems. The discussion and analysis will assist researchers and utility planners in selecting a suitable uncertainty modeling approach with significant penetrations of distributed RESs, which can lead to achieving a reliable and sustainable power system.