Support vector machines (SVMs) are currently state-of-the-art for the classification task and, generally speaking, exhibit good predictive performance due to their ability to model nonlinearities. However, their strength is also their main weakness, as the generated nonlinear models are typically regarded as incomprehensible black-box models. In this paper, we propose a new active learning-based approach (ALBA) to extract comprehensible rules from opaque SVM models. Through rule extraction, some insight is provided into the logics of the SVM model. ALBA extracts rules from the trained SVM model by explicitly making use of key concepts of the SVM: the support vectors, and the observation that these are typically close to the decision boundary. Active learning implies the focus on apparent problem areas, which for rule induction techniques are the regions close to the SVM decision boundary where most of the noise is found. By generating extra data close to these support vectors that are provided with a class label by the trained SVM model, rule induction techniques are better able to discover suitable discrimination rules. This performance increase, both in terms of predictive accuracy as comprehensibility, is confirmed in our experiments where we apply ALBA on several publicly available data sets.