The growing number of applications of machine learning and data mining in many domains—from agriculture to business, education, industrial manufacturing, and medicine—gave rise to new requirements for how to inspect and control the learned models. The research domain of explainable artifcial intelligence (XAI) has been newly established with a strong focus on methods being applied post-hoc on blackbox models. As an alternative, the use of interpretable machine learning methods has been considered—where the learned models are white-box ones. Black-box models can be characterized as representing implicit knowledge—typically resulting from statistical and neural approaches of machine learning, while white-box models are explicit representations of knowledge—typically resulting from rule-learning approaches. In this introduction to the special issue on ‘Explainable and Interpretable Machine Learning and Data Mining’ we propose to bring together both perspectives, pointing out commonalities and discussing possibilities to integrate them.