Lithium-ion batteries (LIBs) have nowadays become outstanding rechargeable energy storage devices with rapidly expanding fields of applications due to convenient features like high energy density, high power density, long life cycle and not having memory effect. Currently, the areas of LIBs are ranging from conventional consumer electronics to electric vehicles (EVs) to aerospace applications. To maintain the demand of widespread application, LIBs with certain specific features are the focus to meet the purpose-oriented requirements. High energy density is one of the prime requirements in the case of vehicular application of LIBs to address the issue of the limited driving range of EVs. The expected acceleration in the commercial growth of EVs is being impeded due to the present level of the driving range offered by the LIB pack. However, this issue can be improved by increasing the energy density of LIBs at the cell level. Because the same size of LIB pack with high energy density LIB cells will deliver a higher amount of power to extend the driving range of EVs. Elevated energy density in the cell level of LIBs can be achieved by either designing LIB cells by selecting suitable materials and combining and modifying those materials through various cell engineering techniques which is a materials-based design approach or optimizing the cell design parameters using a parameter-based design approach. In this paper, a comprehensive review of existing literature on LIB cell design to maximize the energy density with an aim of EV applications of LIBs from both materials-based and cell parameters optimization-based perspectives has been presented including the historical development of LIBs, gradual elevation in the energy density of LIBs, applications of LIBs in EVs, the decreasing trend of LIB cost, and ways of enhancing EV driving range with an outlook of promising battery technologies.