Globally, the research on electric vehicles (EVs) has become increasingly popular due to their capacity to reduce carbon emissions and global warming impacts. The effectiveness of EVs depends on appropriate functionality and management of battery energy storage. Nevertheless, the battery energy storage in EVs provides an unregulated, unstable power supply and has significant voltage drops. To address these concerns, power electronics converter technology in EVs is necessary to achieve a stable and reliable power transmission. Although various EV converters provide significant contributions, they have limitations with regard to high components, high switching loss, high current stress, computational complexity, and slow dynamic response. Thus, this paper presents the emerging trends in analytical assessment of power electronics converter technology incorporated energy storage management in EVs. Hundreds (100) of the most significant and highly prominent articles on power converters for EVs are studied and investigated, employing the Scopus database under predetermined factors to explore the emerging trends. The results reveal that 57% of articles emphasize modeling, experimental work, and performance evaluation. In comparison, 13% of papers are based on problem formulation and simulation analysis, and 8% of articles are survey, case studies, and review-based. Besides, four countries, including China, India, the United States, and Canada, are dominant to publish the maximum articles, indicating 33, 17, 14, and 13, respectively. This review adopts the analytical assessment that outlines various power converters, energy storage, controller, optimization, energy efficiency, energy management, and energy transfer, emphasizing various schemes, key contributions, and research gaps. Besides, this paper discusses the drawbacks and issues of the various power converters and highlights future research opportunities to address the existing limitations. This analytical assessment could be useful to EV engineers and automobile companies towards the development of advanced energy storage management interfacing power electronics for sustainable EV applications.