Network intrusion is a growing threat with potentially severe impacts, which can be damaging in multiple ways to network infrastructures and digital/intellectual assets in the cyberspace. The approach most commonly employed to combat network intrusion is the development of attack detection systems via machine learning and data mining techniques. These systems can identify and disconnect malicious network traffic, thereby helping to protect networks. This chapter systematically reviews two groups of common intrusion detection systems using fuzzy logic and artificial neural networks, and evaluates them by utilizing the widely used KDD 99 benchmark dataset. Based on the findings, the key challenges and opportunities in addressing cyberattacks using artificial intelligence techniques are summarized and future work suggested.