In recent times, the number of computer systems and networks has grown dramatically. These computer systems and networks are now more vulnerable to cyber-attacks than ever before. Due to the complexity and dynamic characteristics of cyber-attacks, computer systems require many cyber-protecting mechanisms. In this article, a review of computational intelligence-based cyber-attack detection methods is presented. The fundamental issues in cybersecurity and attack detection were described before introducing various computational intelligence-based attack detection applications. This review is focused on the cyber-attack detection approaches based on machine learning, deep learning and reinforcement learning techniques. The benchmark datasets used in cyber-attack detection research are first described and the performance of several computational intelligence-based cyber-attack detection methods was compared to validate the attack detection efficiency. Finally, a multi-agent reinforcement learning-based cyber-attack detection method was proposed to improve the attack detection performance when using reinforcement learning.