Today’s systems produce a wealth of data every day, and the data further generates more data, i.e., the derived data, forming into a complex data propagation network, defined as the data’s lineage. There are many reasons for users and administrators to forget certain data including the data’s lineage. From the privacy perspective, a system may leak private information of certain users, and those users unhappy about privacy leaks naturally want to forget their data and its lineage. From the security perspective, an anomaly detection system can be polluted by adversaries through injecting manually crafted data into the training set. Therefore, we envision forgetting systems, capable of completely forgetting certain data and its lineage. In this paper, we focus on making learning systems forget, the process of which is defined as machine unlearning or unlearning. To perform unlearning upon learning system, we present general unlearning criteria, i.e., converting a learning system or part of it into a summation form of statistical query learning model, and updating all the summations to achieve unlearning. Then, we integrate our unlearning criteria into an unlearning architecture that interacts with all the components of a learning system, such as sample clustering and feature selection. To demonstrate our unlearning criteria and architecture, we select four real-world learning systems, including an item-item recommendation system, an online social network spam filter, and a malware detection system. These systems are first exposed to an adversarial environment, e.g., if the system is potentially vulnerable to training data pollution, we first pollute the training data set and show that the detection rate drops significantly. Then, we apply our unlearning technique upon those affected systems, either polluted or leaking private information. Our results show that after unlearning, the detection rate of a polluted system increases back to the one before pollution, and a system leaking a particular user’s private information completely forgets that information.