Idiomatic expressions (Redewendungen) are fixed linguistic units whose overall meaning exceeds the sum of their individual words. When someone says jemandem die Daumen drücken, they are not literally pressing their thumbs together but wishing someone good luck. Mastering these expressions at the C1 level is no longer optional, since they saturate literature, journalism, and informal daily conversation; without them, a learner understands the individual words but misses the intended meaning entirely, sometimes arriving at the exact opposite sense, as with das ist nicht mein Bier, which has nothing to do with beer and simply means "that's not my concern."
These expressions fall into recurring families that make them easier to classify and remember: expressions built on body parts, such as die Nase voll haben ("to be fed up") and sich den Kopf zerbrechen ("to rack one's brain"); expressions drawn from the animal world, such as den Stier bei den Hörnern packen ("to take the bull by the horns"); expressions from nature and the sky, such as auf Wolke 7 schweben ("to be over the moon") and aus allen Wolken fallen ("to be utterly stunned"); and expressions from trades and everyday work, such as in trockenen Tüchern sein ("to be settled and done," originally referring to dry laundry). Recognizing an expression's family aids memory, but it never substitutes for memorizing the complete fixed form, including its prepositions and inflection.
The central warning is that word-for-word translation almost always misleads, because an idiom is a closed semantic unit that cannot be taken apart or have one component swapped for a near-synonym while keeping its meaning. One cannot, for instance, replace die Katze aus dem Sack lassen ("to let the cat out of the bag," i.e., to reveal a secret) with die Katze aus der Tasche lassen on the assumption that Tasche is an acceptable synonym for Sack — an idiom is as fixed in form as a proverb. It is also worth noting that some expressions vary in form or usage across different German-speaking regions, so a phrase common in one place may sound unfamiliar in another.
The most common mistake among advanced learners is trying to guess a new expression's meaning purely from context without verifying it, or using a colloquial expression in a formal setting where it is entirely out of place, since most idioms belong to the informal spoken register and have no place in academic writing or official correspondence.