Detection of anomalies in data is one of the fundamental machine learning tasks. Anomaly detection provides the core technology for a broad spectrum of security-centric applications. In this dissertation, we examine various aspects of anomaly based intrusion detection in computer security. First, we present a new approach to learn program behavior for intrusion detection. Text categorization techniques are adopted to convert each process to a vector and calculate the similarity between two program activities. Then the k-nearest neighbor classifier is employed to classify program behavior as normal or intrusive. We demonstrate that our approach is able to effectively detect intrusive program behavior while a low false positive rate is achieved. Second, we describe an adaptive anomaly detection framework that is de- signed to handle concept drift and online learning for dynamic, changing environments. Through the use of unsupervised evolving connectionist systems, normal behavior changes are efficiently accommodated while anomalous activities can still be recognized. We demonstrate the performance of our adaptive anomaly detection systems and show that the false positive rate can be significantly reduced.