Connected and Cooperative Automated Mobility (CCAM) applications, instrumental in enhancing vehicle communication with infrastructure and the cloud, face cybersecurity vulnerabilities due to their intricate components requiring multifaceted cryptographic validation. With quantum computing advancements, traditional public key cryptography becomes susceptible, emphasizing the need for quantum-resistant algorithms to assure long-term automotive cybersecurity. Although Post-Quantum Cryptography (PQC), which provides solutions to counter this quantum risk is still under research, several algorithms have emerged and are under standardization. This paper provides a comprehensive overview of the status of PQC in automotive applications, including a performance analysis of selected algorithms in this research. Further, it presents some potential use cases of PQC (such as Secure Over-The-Air (SOTA) software update and Vehicle to everything (V2X) communication). By relying on PQC, the automotive industry can stay ahead in securing connected vehicles against emerging quantum computer threats.