Electric and hybrid vehicles have become widespread in large cities due to the desire for environmentally friendly technologies, reduction of greenhouse gas emissions and fuel, and economic advantages over gasoline and diesel vehicles. In electric vehicles, overheating, vibration, or mechanical damage due to collision with an object or another vehicle can lead to the failure of lithium-ion batteries up to thermal runaway and fire. Therefore, the development of battery safety control systems is one of the most important factors contributing to the large-scale electrification of public and private transport. This review examines the design features of the location and management of the battery pack to achieve maximum safety and operational efficiency when using an electric vehicle. The power characteristics and life-cycles of various types of lithium-ion batteries depending on the chemical nature of their electrodes are considered, using the example of commercial vehicles’—Tesla, Nissan Leaf, Porsche Taycan, Zeekr, and Chevrolet Volt—strategic technologies for the placement and packaging of batteries, and battery cooling and monitoring systems (State of Health and State of Charge) are also discussed. In conclusion, the current challenges in the field are summarized and promising research directions are proposed.