Cyber security is one of the most significant challenges in connected vehicular systems and connected vehicles are prone to different cybersecurity attacks that endanger passengers' safety. Cyber security in intelligent connected vehicles is composed of in-vehicle security and security of inter-vehicle communications. Security of Electronic Control Units (ECUs) and the Control Area Network (CAN) bus are the most significant parts of in-vehicle security. Besides, with the development of 4G LTE and 5G remote communication technologies for vehicle-toeverything (V2X) communications, the security of inter-vehicle communications is another potential problem. After giving a short introduction to the architecture of next-generation vehicles including driverless and intelligent vehicles, this review paper identifies a few major security attacks on the intelligent connected vehicles. Based on these attacks, we provide a comprehensive survey of available defences against these attacks and classify them into four categories, i.e. cryptography, network security, software vulnerability detection, and malware detection. We also explore the future directions for preventing attacks on intelligent vehicle systems.