
kleben
to glue
To attach something to another thing using an adhesive.
Ich muss das Poster wieder an die Wand kleben.
I need to glue the poster back onto the wall.
to stick / to glue
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to glue
To attach something to another thing using an adhesive.
Ich muss das Poster wieder an die Wand kleben.
I need to glue the poster back onto the wall.

to stick
To remain attached to a surface because of stickiness, often unintentionally.
Der Honig klebt an meinen Fingern.
The honey is sticking to my fingers.

to be glued to
Colloquial for staying fixed in one place or on one thing and not moving away.
Der Film war so spannend, dass wir an unseren Sitzen klebten.
The film was so exciting that we were glued to our seats.

to glue oneself to
To glue oneself to an object, often a road, as a form of civil disobedience or protest.
Die Klimaaktivisten haben sich auf der Hauptstraße festgeklebt.
The climate activists glued themselves to the main road.
The verb 'kleben' (to stick / to glue) is often used with the preposition 'an' (on/to). The accusative indicates direction (where to?), while the dative describes a fixed location (where?).
Er klebt den Zettel an die Tür.
He glues the note to the door.
Pay attention to the subject of the sentence. If a person is the subject, 'kleben' usually means an active action. If a sticky substance is the subject, it describes a property.
Die Kinder kleben bunte Bilder in ihr Heft.
The children glue colorful pictures into their notebook.
In the colloquial meaning, 'kleben' is often used figuratively. Typical expressions are 'an jemandes Lippen kleben' (to hang on someone's every word) or 'am Bildschirm kleben' (to be glued to the screen).
Die Kinder klebten an seinen Lippen, als er die Geschichte erzählte.
The children hung on his every word as he told the story.
This meaning is very new and is found almost exclusively in the context of climate activism and civil disobedience. The activists are often referred to as 'Klimakleber' (climate gluers).
Die Demonstranten drohten damit, sich auf der Autobahn festzukleben.
The demonstrators threatened to glue themselves to the highway.
In the meaning 'sich aus Protest festkleben' (to glue oneself in place in protest), the verb is always used reflexively with 'sich'. It is usually followed by the preposition 'an' or 'auf' with the dative.
Einige Aktivisten haben sich an einem berühmten Gemälde festgeklebt.
Some activists glued themselves to a famous painting.
to be liable / to stick
For a label, kleben and haften can describe the same existing attachment. Kleben tends to suggest stickiness or adhesive, while haften refers neutrally, and often more matter-of-factly, to firm contact. If the only question is whether the label stays attached, haften is particularly suitable.

Das Etikett klebt wegen seiner klebrigen Rückseite fest auf dem Glas.
The label is firmly stuck to the glass because of its sticky backing.
Das Etikett haftet auch ohne sichtbare Klebstoffreste fest auf dem Glas.
The label adheres firmly to the glass even without any visible adhesive residue.