For a liquid droplet to slide down a solid planar surface, the surface usually has to be tilted above a critical angle of approximately 10°. By contrast, droplets of nearly any liquid "slip" on lubricant-infused textured surfaces - so termed slippery surfaces - when tilted by only a few degrees. The mechanism of how the lubricant alters the static and dynamic properties of the drop remains elusive because the drop-lubricant interface is hidden. Here, we image the shape of drops on lubricant-infused surfaces by laser scanning confocal microscopy. The contact angle of the drop-lubricant interface with the substrate exceeds 140°, although macroscopic contour images suggest angles as low as 60°. Confocal microscopy of moving drops reveals fundamentally different processes at the front and rear. Drops recede via discrete depinning events from surface protrusions at a defined receding contact angle, whereas the advancing contact angle is 180°. Drops slide easily, as the apparent contact angles with the substrate are high and the drop-lubricant interfacial tension is typically lower than the drop-air interfacial tension. Slippery surfaces resemble superhydrophobic surfaces with two main differences: drops on a slippery surface are surrounded by a wetting ridge of adjustable height and the air underneath the drop in the case of a superhydrophobic surface is replaced by lubricant in the case of a slippery surface.