“Frogs are well known to capture fast-moving prey by flicking their sticky tongues out of the mouth. This tongue projection behaviour happens extremely fast which makes frog tongues a biological high-speed adhesive system. The processes at the interface between tongue and prey, and thus the mechanism of adhesion, however, are completely unknown.”
New research (2015) has attempted to experimentally clarify the mechanisms. Which appears to be a combination of viscous stickiness and microstructure adhesion.
See: Frog tongue acts as muscle-powered adhesive tape Royal Society Open Science.
Note: The same puzzle exists for the feet-pads of many insects - which can somehow adhere to almost any surface. Some of the attraction can be explained by Van der Waals forces, but others cannot.