Autonomous driving services depends on active sensing from modules such as camera, LiDAR, radar, and communication units. Traditionally, these modules process the sensed data on high-performance computing units inside the vehicle, which can deploy intelligent algorithms and AI models. The sensors mentioned above can produce large volumes of data, potentially reaching up to 20 Terabytes. This data size is influenced by factors such as the duration of driving, the data rate, and the sensor specifications. Consequently, this substantial amount of data can lead to significant power consumption on the vehicle. Similarly, a substantial amount of data will be exchanged between infrastructure sensors and vehicles for collaborative vehicle applications or fully connected autonomous vehicles. This communication process generates an additional surge of energy consumption. Although the autonomous vehicle domain has seen advancements in sensory technologies, wireless communication, computing and AI/ML algorithms, the challenge still exists in how to apply and integrate these technology innovations to achieve energy efficiency. This survey reviews and compares the connected vehicular applications, vehicular communications, approximation and Edge AI techniques. The focus is on energy efficiency by covering newly proposed approximation and enabling frameworks. To the best of our knowledge, this survey is the first to review the latest approximate Edge AI frameworks and publicly available datasets in energy-efficient autonomous driving. The insights from this survey can benefit the collaborative driving service development on low-power and memory-constrained systems and the energy optimization of autonomous vehicles.@en