Movement-independent trapping mechanisms are based on stickiness, slipperiness, and direction-dependent mechanical obstruction. Here, the implementation of these principles in flypaper, pitfall, and eel traps is discussed in the light of recent scientific advances. The chemical composition and rheological properties of trapping fluids, and the (micro-) morphology of trapping surfaces, are related to their functions. Recent discoveries including the role of surface wettability in prey capture by pitcher plants are presented, and the ecological implications of temporal variations of trap performance and promising directions for future research are discussed.