In an internet-of-things (IoT) environment, cloud computing is emerging as a technologically feasible and economically viable solution for supporting real-time and non-real-time connected vehicle (CV) applications due to its unlimited storage, enormous computing capabilities, and cost advantage, i.e., cloud computing costs less than owning such systems. However, maintaining cybersecurity is a major challenge in cloud-supported CV applications as it requires CVs and various transportation or non-transportation services to exchange data with the cloud via multiple wired and wireless communication networks, such as long-term evolution (LTE) and Wi-Fi. In this paper, we review the cybersecurity requirements of cloud-supported CV applications, such as confidentiality, integrity, availability, authentication, accountability, and privacy. Our review also identifies the associated cybersecurity challenges that might impact cloud-supported CV applications and corresponding solutions to these challenges. In addition, we present future research opportunities to prevent and mitigate cybersecurity issues in cloud computing for CV-related applications.