Paintings deteriorate over time due to aging and storage conditions, with cracks being a common form of degradation. Detecting and mapping these cracks is crucial for art analysis and restoration but it presents challenges. Traditional methods often require tedious manual effort, while deep learning (DL) relies on large annotated datasets, which are expensive to produce. Also, DL does not generalize well, in the sense that it is conditioned by the properties of the training data and often performs poorly on unseen data with slightly different properties. To address these issues, we developed a deep active learning (DAL) method called DAL4ART. DAL methods start with minimal annotated data, perform their task, and then retrain iteratively on newly annotated samples to improve efficiency. This iterative learning process makes our method require less data, learn progressively from human input, handle partially annotated data, and perform better on previously unseen paintings. Additionally, our method can integrate various imaging modalities and is equipped with a user-friendly web interface. We demonstrate the application of the proposed crack detection tool in a concrete use case as a means of supporting the restoration of old master paintings.