Autonomous vehicles (AV) are expected to improve, reshape, and revolutionize the future of ground transportation. It is anticipated that ordinary vehicles will one day be replaced with smart vehicles that are able to make decisions and perform driving tasks on their own. In order to achieve this objective, self-driving vehicles are equipped with sensors that are used to sense and perceive both their surroundings and the faraway environment, using further advances in communication technologies, such as 5G. In the meantime, local perception, as with human beings, will continue to be an effective means for controlling the vehicle at short range. In the other hand, extended perception allows for anticipation of distant events and produces smarter behavior to guide the vehicle to its destination while respecting a set of criteria (safety, energy management, traffic optimization, comfort). In spite of the remarkable advancements of sensor technologies in terms of their effectiveness and applicability for AV systems in recent years, sensors can still fail because of noise, ambient conditions, or manufacturing defects, among other factors; hence, it is not advisable to rely on a single sensor for any of the autonomous driving tasks. The practical solution is to incorporate multiple competitive and complementary sensors that work synergistically to overcome their individual shortcomings. This article provides a comprehensive review of the state-of-the-art methods utilized to improve the performance of AV systems in short-range or local vehicle environments. Specifically, it focuses on recent studies that use deep learning sensor fusion algorithms for perception, localization, and mapping. The article concludes by highlighting some of the current trends and possible future research directions.