In recent years, advancements in the field of the artificial intelligence (AI) gained a huge momentum due to the worldwide appliance of this technology by the industry. One of the crucial areas of AI are neural networks (NN), which enable commercial utilization of functionalities previously not accessible by usage of computers. Intrusion detection system (IDS) presents one of the domains in which neural networks are widely tested for improving overall computer network security and data privacy. This article gives a thorough overview of recent literature regarding neural networks usage in intrusion detection system area, including surveys and new method proposals. Short tutorial descriptions of neural network architectures, intrusion detection system types and training datasets are also provided.