The rapid evolution of mobile devices, their applications, and the amount of data generated by them causes a significant increase in bandwidth consumption and congestions in the network core. Edge Computing offers a solution to these performance drawbacks by extending the cloud paradigm to the edge of the network using capable nodes of processing compute-intensive tasks. In the recent years, vehicular edge computing has emerged for supporting mobile applications. Such paradigm relies on vehicles as edge node devices for providing storage, computation, and bandwidth resources for resource-constrained mobile applications. In this article, we study the challenges of computation offloading for vehicular edge computing. We propose a new classification for the better understanding of the literature designing vehicular edge computing. We propose a taxonomy to classify partitioning solutions in filter-based and automatic techniques; scheduling is separated in adaptive, social-based, and deadline-sensitive methods, and finally data retrieval is organized in secure, distance, mobility prediction, and social-based procedures. By reviewing and analyzing literature, we found that vehicular edge computing is feasible and a viable option to address the increasing volume of data traffic. Moreover, we discuss the open challenges and future directions that must be addressed towards efficient and effective computation offloading and retrieval from mobile users to vehicular edge computing.