Securing safe-driving for connected and autonomous vehicles (CAVs) continues to be a widespread concern despite various sophisticated functions delivered by artificial intelligence for in-vehicle devices. Besides, diverse malicious network attacks become ubiquitous along with the worldwide implementation of the Internet of Vehicles, which exposes a range of reliability and privacy threats for managing data in CAV networks. Combined with the fact that the capability of existing CAVs in handling intensive computation tasks is limited, this implies a need for designing an efficient assessment system to guarantee autonomous driving safety without compromising data security. Motivated by this, in this article, we propose a novel framework, namely Blockchain-enabled intElligent Safe-driving assessmenT (BEST), that offers a smart and reliable approach for conducting safe driving supervision while protecting vehicular information. Specifically, a promising solution that exploits a long short-term memory model is introduced to assess the safety level of the moving CAVs. Then, we investigate how a distributed blockchain obtains adequate trustworthiness and robustness for CAV data by adopting a byzantine fault tolerance-based delegated proof-of-stake consensus mechanism. Simulation results demonstrate that our presented BEST gains better data credibility with a higher prediction accuracy for vehicular safety assessment when compared with existing schemes. Finally, we discuss several open challenges that need to be addressed in future CAV networks.