Physical and biological nanoscale systems and associated quantum phenomena are ubiquitous in nature and a man-made world. Today, they are becoming critically important in many key areas of human well-being, including environmental sustainability, alternative energy sources, and medicine. State-of-the-art approaches and methods of mathematics with the development and analysis of coupled mathematical models in this field provide a fundamental ingredient for our better understanding of such systems and their efficient applications. By bringing together some of the world’s leading researchers in the field, this focus program is devoted to the study of such systems, their mathematical analysis, modelling, and applications.