The cyber threat landscape is rapidly evolving, with attacks increasing in sophistication, volume, and targeting precision. Artificial Intelligence (AI) is essential to cybersecurity, enabling the analysis of massive amounts of data, the identification of complex anomalies such as zero-day threats, and response speeds beyond traditional methods. Despite the plethora of successes of AI-based techniques in realizing enhanced Intrusion Detection System (IDS), existing research trained on static datasets struggles against dynamic threats and quickly becomes obsolete. Addressing this limitation requires a paradigm shift towards learning systems capable of continuous adaptation. Continual Learning, also known as Lifelong Learning, provides a robust solution to realize a system designed for incremental adaptation over time, it allows IDS to continuously adapt to new data and emerging threats without forgetting past knowledge. Crucially, the effective realization of such systems hinges on sophisticated mathematical optimization techniques. These methods are essential for efficiently updating model parameters with new data while mitigating catastrophic forgetting – the tendency of neural networks to abruptly forget previously learned information. The careful selection and implementation of optimization algorithms, loss functions, and regularization strategies become paramount in ensuring stable and accurate long-term learning. The focus is on realizing systems that effectively manage these challenges. For practical realization, it is also critical that these advanced IDSs are highly optimized for resource efficiency and computational performance. The goal is to realize IDS that maintain high accuracy and resilience over the long term, overcoming a key weakness of current systems and promising more adaptive, constantly updated defenses against the ever-increasing tide of cyber attacks.