The surface tension of partially wetting droplets deforms soft substrates. These deformations are usually localized to a narrow region near the contact line, forming a so-called elastocapillary ridge.' When a droplet slides along a substrate, the movement of the elastocapillary ridge dissipates energy in the substrate and slows the droplet down. Previous studies have analyzed isotropically spreading droplets and found that the advancing contact line surfs’ the elastocapillary ridge, with a velocity determined by a local balance of capillary forces and bulk rheology. Here, we experimentally explore the dynamics of a droplet sliding across soft substrates. At low velocities, the contact line is nearly circular, and dissipation increases logarithmically with speed. At higher droplet velocities, the contact line adopts a bullet-like shape, and the dissipation levels off. At the same time, droplets shed a pair of `elastocapillary rails’ that fade away slowly behind it. These results suggest that droplets favor sliding along a stationary ridge over surfing atop a translating one.

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