In a series of recent papers, Prof. Olariu and his co-workers have promoted the vision of vehicular clouds (VCs), a nontrivial extension, along several dimensions, of conventional cloud computing. In a VC, underutilized vehicular resources including computing power, storage, and Internet connectivity can be shared between drivers or rented out over the Internet to various customers. Clearly, if the VC concept is to see a wide adoption and to have significant societal impact, security and privacy issues need to be addressed. The main contribution of this work is to identify and analyze a number of security challenges and potential privacy threats in VCs. Although security issues have received attention in cloud computing and vehicular networks, we identify security challenges that are specific to VCs, e.g., challenges of authentication of high-mobility vehicles, scalability and single interface, tangled identities and locations, and the complexity of establishing trust relationships among multiple players caused by intermittent short-range communications. Additionally, we provide a security scheme that addresses several of the challenges discussed.