As an emerging computing paradigm, the Internet of Vehicles (IoV) brings a lot of benefits for drivers and consumers, such as route recommendation, reducing traffic congestion, and parking difficulty. However, participants in IoV are inevitably exposed to privacy threats because their data are outsourced to a third party. This article presents a comprehensive analysis of the root causes of privacy risks in IoV and the potential solutions. We begin by introducing the concrete privacy challenges, which are tied to the structural properties of IoV. Then, we present a unified framework of data privacy preservation in IoV, which integrates multiple privacy techniques, including encryption, anonymity, and perturbation. Next, we investigate the possible research directions for route recommendation, charging deployment, traffic prediction under different privacy requirements in detail. Finally, we discuss emerging techniques and environments (e.g., blockchain, smart grid, and 5G communication) to strengthen the ability and application of IoV under strong protection.