What does it mean to “see” atoms? How have we reached a stage in which it is possible to perform microscopy down to the atomic level? And what do we learn by doing this? The fascinating story that will explain this involves a question that has long been debated in Oxford, dating back to the seventeenth century when Robert Hooke became one of the first practitioners of the optical microscope: is light a particle or a wave? In the twentieth century, physicists asked the same question of electrons. The modern microscopy techniques that will be described utilise an effect called tunnelling, in which particles can behave like ghostlike entities, passing through solid walls. It’s often described as a counter-intuitive quantum mechanical effect, but in fact originates in classical nineteenth century physics. Now these methods are being used to unravel the mysteries surrounding the newly discovered materials of the twenty-first century, whose behaviour is fundamentally quantum-mechanical.