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The nepenthes-inspired lubricant-infused surface (LIS) is emerging as a novel repellent surface with self-healing, self-cleaning, pressure stability and ultra-slippery properties. Recently, stimuli-responsive materials to construct a smart LIS have broadened the application of LIS for droplet manipulation, showing great promise in microfluidics. This review mainly focuses on the recent developments towards the droplet manipulation on LIS with different mechanisms induced by various external stimuli, including thermo, light, electric, magnetism, and mechanical force. First, the droplet condition on LIS, determined by the properties of the droplet, the lubricant and substrate, is illustrated. Droplet manipulation via altering the droplet regime realized by different mechanisms, such as varying slipperiness, electrostatic force and wettability, is discussed. Moreover, some applications on droplet manipulation employed in various filed, including microreactors, microfluidics, etc., are also presented. Finally, a summary of this work and possible future research directions for the transport of droplets on smart LIS are outlined to promote the development of this field.