Artificial Intelligence (AI) has found increasing application in various domains, revolutionizing problem-solving and data analysis. However, in decision-sensitive areas like Intrusion Detection Systems (IDS), trust and reliability are vital, posing challenges for traditional black box AI systems. These black box IDS, while accurate, lack transparency, making it difficult to understand the reasons behind their decisions. This dissertation explores the concept of eXplainable Intrusion Detection Systems (X-IDS), addressing the issue of trust in X-IDS. It explores the limitations of common black box IDS and the complexities of explainability methods, leading to the fundamental question of trusting explanations generated by black box explainer modules. To address these challenges, this dissertation presents the concept of white box explanations, which are innately explainable. While white box algorithms are typically simpler and more interpretable, they often sacrifice accuracy. However, this work utilized white box Competitive Learning (CL), which can achieve competitive accuracy in comparison to black box IDS. We introduce Rule Extraction (RE) as another white box technique that can be applied to explain black box IDS. It involves training decision trees on the inputs, weights, and outputs of black box models, resulting in human-readable rulesets that serve as global model explanations. These white box techniques offer the benefits of accuracy and trustworthiness, which are challenging to achieve simultaneously. This work aims to address gaps in the existing literature, including the need for highly accurate white box IDS, a methodology for understanding explanations, small testing datasets, and comparisons between white box and black box models. To achieve these goals, the study employs CL and eclectic RE algorithms. CL models offer innate explainability and high accuracy in IDS applications, while eclectic RE enhances trustworthiness. The contributions of this dissertation include a novel X-IDS architecture featuring Self-Organizing Map (SOM) models that adhere to DARPA’s guidelines for explainable systems, an extended X-IDS architecture incorporating three CL-based algorithms, and a hybrid X-IDS architecture combining a Deep Neural Network (DNN) predictor with a white box eclectic RE explainer. These architectures create more explainable, trustworthy, and accurate X-IDS systems, paving the way for enhanced AI solutions in decision-sensitive domains.