We show how anisotropic, grooved features facilitate the trapping and directed transport of droplets on lubricated, liquid-shedding surfaces. Capillary action pins droplets to topographic surface features, enabling transport along the feature while inhibiting motion across (or detachment from) the feature. We demonstrate the robustness of this capillary-based mechanism for directed droplet transport on slippery surfaces by combining experiments on synthetic, lubricant-infused surfaces with observations on the natural trapping surface of a carnivorous pitcher plant.Controlling liquid navigation on synthetic surfaces promises to unlock significant potential in droplet-based technologies. Our observations also offer novel insight into the evolution of the Nepenthes pitcher plant, indicating that the 'pitfall' trapping mechanism is enhanced by the lubricant-infused, macroscopic grooves on the slippery peristome surface, which guide prey into the trap in a way that is more tightly controlled than previously considered.