Vehicles in Internet of Vehicles (IoV) exchange information about location, environment, infotainment, as well as social information with other units via vehicular communication networks. This makes IoV with key social entities in the human-vehicle-infrastructure-roadside units (RSUs) as integrated intelligent transportation systems. Therefore, by identifying the cyber-physical-social features of IoV and presenting its complexity issues of both engineering and social dimensions, this article proposes and introduces the concept, architecture, and applications of parallel IoV (PIoV). Three main components of PIoV are demonstrated, which are artificial IoV to learn and describe the physical IoV, computation experiments to evaluate and predict the consequences and values of driving strategies, and parallel execution to prescribe the operation of the physical IoV. PIoV makes it possible to achieve safe, smart, effective, and efficient transportation management and control. The final objective of PIoV is to equip IoV with descriptive, predictive, and prescriptive intelligence based on the parallel intelligence approach.