Icicles are harmless and picturesque winter phenomena, familiar to anyone who lives in a cold climate. The shape of an icicle emerges from a subtle feedback between ice formation, which is controlled by the release of latent heat, and the flow of water over the evolving shape. The water flow, in turn, determines how the heat flows. The air around the icicle is also flowing, and all forms of heat transfer are active in the air. Icicles often exhibit ripples or ribs around their circumference, which are the result of a poorly understood morphological instability. The wavelength of the ripples is remarkably independent of the growing conditions. Similar shape and ripple phenomena are also observed on stalactites, although certain details of their formation differ. We built a laboratory icicle growing machine to explore the fluid mechanics of icicle formation. We learned what it takes to make an ideal icicle and the surprisingly subtle origin of the ripples.