The progress in the field of computer networks and internet is increasing with tremendous volume in recent years. This raises important issues concerning security. Several solutions emerged in the past, which provide security at the host or network level. These traditional solutions like antivirus, firewall, spyware and authentication mechanism provide security to some extents but they still face the challenges of inherent system flaws and social engineering attacks. Some interesting solution emerged like intrusion detection and prevention systems but these too have some problems like detecting and responding in real time and discovering novel attacks. Because the network intrusion behaviors are characterized with uncertainty, complexity and diversity, an intrusion detection method based on neural network and Particle Swarm Optimization (PSO) algorithm is widely used in order to address the problem. This paper gives an insight into how PSO and its variants can be combined with various neural network techniques in order to be used for anomaly detection in network intrusion detection system in order to enhance the performance of intrusion detection system.