Sensors and intelligent applications enabling smart vehicular traffic create an opportunity for improving the welfare of people, from the viewpoints of efficiency, sustainability, and social inclusivity. Like the opportunities, challenges of such an endeavour are multifaceted, including the scalable collection and processing of the hefty data volumes generated by sensors, and the coordinated operation between selfish agents. The purpose of this work is to survey recent literature with an emphasis on applications and a multidisciplinary eye, with the aim of stimulating discussion and reflection in the scientific communities. The principal application areas of smart traffic and smart mobility are discussed, synthesizing different perspectives. Many intriguing areas for future research exist besides those relative to connectivity, data fusion, and privacy. Some research challenges pertinent to sustainability, insurance, simulation and the handling of ambiguous information are highlighted.