Electric vehicles are widely adopted globally as a sustainable mode of transportation. With the increased availability of onboard computation and communication capabilities, vehicles are moving towards automated driving and intelligent transportation systems. The adaption of technologies such as IoT, edge intelligence, 5G, and blockchain in vehicle architecture has increased possibilities towards efficient and sustainable transportation systems. In this article, we present a comprehensive study and analysis of the edge computing paradigm, explaining elements of edge AI. Furthermore, we discussed the edge intelligence approach for deploying AI algorithms and models on edge devices, which are typically resource-constrained devices located at the edge of the network. It mentions the advantages of edge intelligence and its use cases in smart electric vehicles. It also discusses challenges and opportunities and provides in-depth analysis for optimizing computation for edge intelligence. Finally, it sheds some light on the research roadmap on AI for edge and AI on edge by dividing efforts into topology, content, service segments, model adaptation, framework design, and processor acceleration, all of which stand to gain advantages from AI technologies. Investigating the incorporation of important technologies, issues, opportunities, and Roadmap in this study will be a valuable resource for the community engaged in research on edge intelligence in electric vehicles.