Refraction is one of the most fundamental phenomena in nature. It gives rise to such well-known effects as the apparent bending of objects partly immersed in water, rainbows, mirages, green flashes, and haloes. Refraction is also utilized in many existing optical instruments, including microscopes, telescopes, and eyeglasses. All these phenomena and applications rely on conventional or “positive” refraction. What would the world look like if the sign of refraction were reversed?