Despite the expanded efforts, the vehicular ad-hoc networks (VANETs) are still facing many challenges such as network performances, network scalability and context-awareness. Many solutions have been proposed to overcome these obstacles, and the edge computing, an extension of the cloud computing, is one of them. With edge computing, communication, storage and computational capabilities are brought closer to end users. This could offer many benefits to the global vehicular network including, for example, lower latency, network off-loading and context-awareness (location, environment factors, etc.). Different approaches of edge computing have been developed: mobile edge computing (MEC), fog computing (FC) and cloudlet are the main ones. After introducing the vehicular environment background, this paper aims to study and compare these different technologies. For that purpose their main features are compared and the state-of-the-art applications in VANETs are analyzed. In addition, MEC, FC, and cloudlet are classified and their suitability level is debated for different types of vehicular applications. Finally, some challenges and future research directions in the fields of edge computing and VANETs are discussed.