Geckos (small reptiles of the family Gekkonidae ) can walk upside-down on almost any surface due to the microscopic hairs - called setae - on their toe pads.

Since the discovery of the molecular Van der Waals Force - which causes very closely-aligned surfaces to attract (and repel) each other - it has been widely assumed that the micro- and nano-scale setae were exploiting the force for adhesion. (The pads aren't 'sticky' in the usual sense of the word, but are dry rather than wet-adhesive)

A 2014 study published in the Journal of the Royal Society, Interface, suggested, however, that the predominant attractive force is instead being provided by an electrostatic interaction called the Contact Electrification (CE) phenomenon.

[…] we have demonstrated that it is the CE-driven electrostatic interactions which dictate the strength of gecko adhesion, and not the van der Waals or capillary forces which are conventionally considered as the main source of gecko adhesion.

Source :Role of contact electrification and electrostatic interactions in gecko adhesion Journal of the Royal Society, Interface, 11(98)

For details of the alternative Van der Waals theory, see Wikipedia