There has been incredible progress in the field of ultrafast STM (USTM) in recent years, including the emergence of new technological concepts such as single-cycle lightwave-driven tunneling and rectification or plasmon-driven tunneling in optical USTM. This review provides a comprehensive summary of the field, focusing on the classification of light-matter interaction in tunnel junctions and approaches to image ultrafast electronic and structural excitations on solid surfaces. Questions addressed include: What are useful approaches to classify the interaction of tunnel junctions with time-varying electromagnetic fields? What types of ultrafast tunnel currents can occur in USTM? What information about the transient state of the sample, and what physical insights can be gained? By discussing these questions, the article aims to provide a solid foundation to the further establishment of USTM as a valuable tool for ultrafast surface science. Progr. Surf. Sci. 2023, in press.