Glancing has a special affinity with surfaces, which draw its spontaneous attention with a special allure and force. What it picks up on surfaces – primarily visual ones but auditory and tactile as well (glancing occurs in aural as well as haptic modalities) – is often something it did not expect. When that happens, a unique kind of surprise is precipitated: however demure and gentle it may be, it may also illuminate existing puzzles as well as offer guideposts for further exploration. In this essay I investigate the triadic conjunctio between glance, surface, and surprise that deserves more phenomenological consideration than it has so far received. The direction of thought opened here is pursued in more detail in my book The World at a Glance (2007).