With the advances in information technology (IT) criminals are using cyberspace to commit numerous cyber crimes. Cyber infrastructures are highly vulnerable to intrusions and other threats. Physical devices and human intervention are not sufficient for monitoring and protection of these infrastructures; hence, there is a need for more sophisticated cyber defense systems that need to be flexible, adaptable and robust, and able to detect a wide variety of threats and make intelligent real-time decisions. Numerous bio-inspired computing methods of Artificial Intelligence have been increasingly playing an important role in cyber crime detection and prevention. The purpose of this study is to present advances made so far in the field of applying AI techniques for combating cyber crimes, to demonstrate how these techniques can be an effective tool for detection and prevention of cyber attacks, as well as to give the scope for future work.