Scientific advancements, their application through technological development, and world politics have been long acknowledged as affecting each other, and are today more than ever at the heart of global policy. Speaking of ‘science diplomacy’ as the encounter of world politics and the world of science at the heart of these advancements might be a unique window into our time. This potential is what prompts this special issue to gather views from a variety of scholarly and practical viewpoints, linking the well‐established world of reflective practitioners in science diplomacy to the growing field of international relations (IR) scholars theorising this realm. Can speaking of ‘science diplomacy’ situate our attention at the crossroads of science and international relations, and spur greater appreciation for their intersections? This introduction to the special issue summarises the rise of science diplomacy as field of inquiry, and casts questions as to the need to advance, where not reform, these conceptualisations. It defines science diplomacy as a ‘boundary problem’ par excellence and emphasises its ‘productive tension’ that emerges between the various ways of knowing of actors belonging to ‘different social worlds’, seeking to gather a productive tension of views on this theme in the issue.