Recent advances in information technology have revolutionized the automotive industry, paving the way for next-generation smart vehicular mobility. Specifically, vehicles, roadside units, and other road users can collaborate to deliver novel services and applications that leverage, for example, big vehicular data and machine learning. Relatedly, fifth-generation cellular networks (5G) are being developed and deployed for low-latency, high-reliability, and high bandwidth communications. While 5G adjacent technologies such as edge computing allow for data offloading and computation at the edge of the network thus ensuring even lower latency and context-awareness. Overall, these developments provide a rich ecosystem for the evolution of vehicular applications, communications, and computing. Therefore 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. In particular, this paper highlights several vehicular applications, investigates their requirements, details the enabling communication technologies and computing paradigms, and studies data analytics pipelines and the integration of these enabling technologies in response to application requirements.