verdrehen
to twist
To move something out of its normal shape or position by twisting; to sprain or wrench something.
Ich bin beim Sport unglücklich gefallen und habe mir das Knie verdreht.
I fell awkwardly while doing sports and twisted my knee.

to twist / distort
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to twist
To move something out of its normal shape or position by twisting; to sprain or wrench something.
Ich bin beim Sport unglücklich gefallen und habe mir das Knie verdreht.
I fell awkwardly while doing sports and twisted my knee.

'Verdrehen' (to twist / distort) is an inseparable verb. The prefix 'ver-' remains firmly attached to the stem 'drehen' (to turn) in all tenses and sentence constructions. It often indicates that something is being made wrong or brought into a bad state.
Er hat die Fakten in seiner Aussage komplett verdreht.
He completely distorted the facts in his statement.
When someone injures a body part, 'verdrehen' (to twist) is used reflexively. The person is in the dative, and the body part is in the accusative: 'sich (dative) etwas (accusative) verdrehen' (to twist something).
Die Sportlerin hat sich im Spiel den Knöchel verdreht.
The athlete twisted her ankle during the game.
When it is about lying or manipulation, 'verdrehen' (to distort) is used with abstract nouns such as 'die Wahrheit' (the truth), 'die Tatsachen' (the facts), or 'die Worte' (the words). A fixed expression is 'jemandem die Worte im Mund verdrehen' (to twist someone's words).
Hör auf, mir die Worte im Mund zu verdrehen! Das habe ich so nicht gesagt.
Stop twisting my words! That's not what I said.
The expression 'die Augen verdrehen' (to roll one's eyes) is a fixed unit. It always expresses annoyance, irritation, or impatience, and the object is always 'die Augen' (the eyes).
Als er die gleiche Frage zum dritten Mal stellte, verdrehte sie genervt die Augen.
When he asked the same question for the third time, she rolled her eyes in annoyance.
to turn / film
'drehen' and 'verdrehen' look similar, and both have to do with movement or change through turning. 'Drehen' is usually neutral: you move something in a circular way or around an axis, or a topic revolves around something. 'Verdrehen', on the other hand, means that something is made wrong, crooked, or distorted by turning. This can be physical, for example a foot, or figurative, when someone misrepresents a statement. The risk of confusion comes from the shared word stem. Remember: 'drehen' is the normal movement; 'verdrehen' makes something wrong or changes the meaning.

Der Journalist hat meine Worte verdreht und etwas anderes daraus gemacht.
The journalist distorted my words and turned them into something else.
Bitte dreh den Schlüssel langsam nach rechts.
Please turn the key slowly to the right.