The goal of this systematic and broad survey is to present and discuss the main challenges that are posed by the implementation of Artificial Intelligence and Machine Learning in the form of Artificial Neural Networks in Cybersecurity, specifically in Intrusion Detection Systems. Based on the results of the state-of-the-art analysis with a number of bibliographic methods, as well as their own implementations, the authors provide a survey of the answers to the posed problems as well as effective, experimentally-found solutions to those key issues. The issues include hyperparameter tuning, dataset balancing, increasing the effectiveness of an ANN, securing the networks from adversarial attacks, and a range of non-technical challenges of applying ANNs for IDS, such as societal, ethical and legal dilemmas, and the question of explainability. Thus, it is a systematic review and a summary of the body of knowledge amassed around implementations of Artificial Neural Networks in Network Intrusion Detection, guided by an actual, real-world implementation.