How does glue actually stick things together?

Glue sticks because it first spreads over a surface, then hardens, and in between it holds on in ways that work at the scale of molecules. An effective adhesive must do three things: wet the base material, meaning keep contact with the solid surface the way a liquid does; increase in strength after it is applied; and transmit load between the two surfaces it joins.

Holding on can happen in more than one way. In mechanical adhesion, the glue works its way into small pores of the surface and locks in. In other cases, electrostatic forces, as in static electricity, hold the substances together. A third mechanism involves the van der Waals forces that develop between molecules. Real glues often use several of these at once.

The hardening step differs from glue to glue. White glue and rubber cement are solvent-based, so they harden as the solvent evaporates. Hot melt adhesives are thermoplastics applied molten, between 65 and 180 °C, and solidify on cooling to make strong bonds between a wide range of materials. Moisture-curing glues, including cyanoacrylates, cure when they react with moisture on the surface or in the air. Two-part glues are not adhesive until you mix them: the components react with each other and show full adhesion only on curing.

Humans worked this out a very long time ago. Around 200,000 years ago, Neanderthals made tar from birch bark and used it to bind stone tools to wooden handles. Later, Middle Stone Age humans added red ochre to plant gum, which made it stronger and kept it from disintegrating when wet. The tape and sticky note on your desk are descendants of the same idea: stick first, hold on second.