Nature has been a constant inspiration in human civilization to achieve technological developments. Recently, the study on nature-inspired materials has expanded to micro- and nanoscale, facilitating new breakthroughs on the design of materials with unique properties. Various types of superhydrophobic surfaces inspired by lotus/rice leaf are examples of nature-inspired surfaces with special wettability. A new class of functional surfaces which are inspired by pitcher plant are the slippery liquid-infused porous surfaces (SLIPS). This review summarizes the properties, design criteria, fabrication strategies, and working mechanisms of both surfaces with specific focus on SLIPS. The application of SLIPS in the field of membrane technology (slippery liquid-infused membranes (SLIMs)) are also reviewed. The design criteria, fabrication methods and applications of SLIMs are discussed in detail. These membranes are also known as liquid gating membranes due to the gating functionality of the capillary-stabilized liquid in the membrane pores leading to a smart gating mechanism. Similarly to the gating ion channels in biological systems, the pores open and close in response to the ambient stimuli, e.g., pressure, temperature, and ions. Different types of stimuli-responsive smart gating membranes are introduced here, and their properties and applications are reviewed in detail. Finally, challenges and perspectives on both SLIPS as well as smart gating membranes are discussed. This review provides a thorough knowledge and practical orientation on nature-inspired functional surfaces and membranes to pave the way for future research and further developments in this emerging field.