Recent advances in information technology have revolutionized the automotive industry, paving the way for next-generation smart vehicular mobility. Vehicles, roadside units, and other road users can collaborate to deliver novel services and applications. These services and applications require 1) massive volumes of heterogeneous and continuous data to perceive the environment, 2) reliable and low-latency communication networks, 3) real-time data processing that provides decision support under application-specific constraints. Addressing such constraints introduces significant challenges for current communication and computing technologies. Relatedly, the fifth generation of cellular networks (5G) was developed to respond to communication challenges by providing for low-latency, high-reliability, and high bandwidth communications. As a major part of 5G, edge computing allows data offloading and computation at the edge of the network, ensuring low-latency and context-awareness, and 5G efficiency. In this work, we aim at providing a comprehensive overview of the state of research on vehicular computing in the emerging age of 5G and big data.