Optical phenomena visible to everyone have been central to the development of, and abundantly illustrate, important concepts in science and mathematics. The phenomena considered include rainbows, sparkling reflections on water, mirages, green flashes, earthlight on the moon, glories, daylight, crystals, and the squint moon. The concepts include refraction, caustics (focal singularities of ray optics), wave interference, numerical experiments, mathematical asymptotics, dispersion, complex angular momentum (Regge poles), polarization singularities, Hamilton’s conical intersections of eigenvalues (‘Dirac points’), geometric phases, and visual illusions.