The automotive industry is developing trends in autonomous driving and connected vehicular systems. These vehicles can access and send the data, download the software updates, connect with other vehicles or other IoT devices via the internet or wireless communication. Autonomous vehicle control urges very strict requirements about the security of the communication channels used by the vehicle to exchange information and the control logic that performs complex driving tasks. So, the increased connectivity results in a heightened risk of a cyber-security attack. For maintaining the advances in safe communication, it is important to establish strong security for connected vehicular systems. For this, existing cybersecurity attacks must be considered to minimize future cybersecurity risks in the connected and autonomous vehicle systems. In this chapter, the authors will emphasize recent works on how autonomous vehicles can ensure strong operation under ongoing cyber security attacks and their possible solutions.