The collection of articles in this special issue is intended to summarize and review the research carried out within the NCCR MUST and also to give perspectives for future research directions. For centuries, scientists have used theoretical modeling and imaging techniques to understand things invisible to the naked eye and thus advance our knowledge. New theoretical and experimental tools foster new science and new science requires new tools. No matter which perspective one takes, there has been, and always will be, a strong interplay between theoretical, technological, and scientific advancements. Today's requirements on theory and imaging tools have increased well beyond the known, and new frontiers in physics, chemistry, and biochemistry demand the ability to theoretically model and visualize events evolving on ultrafast time and nanoscopic length scales. As a result, MUST scientists are constantly pushing the limits of ultrafast theoretical and experimental visualization tools in pursuit of understanding electronic, atomic, and molecular dynamics and their correlations in space and time.