Vehicles will be wirelessly connected in the future, and they will be able to exchange information with other vehicles and their surroundings for safer and more efficient driving. 5G communication systems have introduced advanced functionalities and radio solutions to support connected, cooperative, and automated mobility (CCAM) services with demanding quality of service requirements. However, interoperability among involved stakeholders, seamless connectivity, and the uninterrupted delivery of real-time services across borders are issues that should be carefully analyzed for the realization of cross-border CCAM services. This article provides an overview of key standardization bodies by analyzing recent work on key technologies to provide cross-border connectivity services for CCAM. Standardization gaps and regulatory barriers that may affect fast and efficient adoption of 5G-enabled CCAM services are also discussed.