die Rache
revenge
An action by which someone is deliberately harmed in return for an injustice or insult suffered; retaliation.
Aus Angst vor der Rache seiner Feinde verließ er die Stadt.
Out of fear of his enemies' revenge, he left the city.

revenge
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revenge
An action by which someone is deliberately harmed in return for an injustice or insult suffered; retaliation.
Aus Angst vor der Rache seiner Feinde verließ er die Stadt.
Out of fear of his enemies' revenge, he left the city.

To express the reason for the revenge, use 'aus Rache' (out of revenge) for the motive or 'Rache für' + accusative (revenge for) for the specific occasion. The target of the revenge is connected with 'an' + dative.
Er handelte aus blinder Rache.
He acted out of blind revenge.
Common verbs used in connection with 'Rache' (revenge) are 'Rache üben' (to exact revenge) and 'auf Rache sinnen' (to plot revenge).
Der verstoßene Prinz sann auf Rache an seinem Bruder.
The banished prince plotted revenge against his brother.
'Rache' (revenge) is often described with certain adjectives that specify its nature. Common combinations are 'süße Rache' (sweet revenge), 'grausame Rache' (cruel revenge), or 'persönliche Rache' (personal revenge).
Für ihn war es die süße Rache, am Ende doch noch zu gewinnen.
For him, it was sweet revenge to end up winning after all.
The expression 'Rache nehmen' (to take revenge) is the most active and common way to express the action. The person on whom one takes revenge is always in the dative, introduced by the preposition 'an'.
Sie schwor, an dem Dieb Rache zu nehmen.
She swore to take revenge on the thief.
punishment / penalty
'die Strafe' and 'die Rache' both have to do with a negative reaction to wrong or hurtful behavior. The important difference is this: a punishment often comes from a person or institution that has the authority to give it, for example a court, a teacher, or parents. Revenge is more personal. In that case, someone wants to harm another person because they feel hurt or unfairly treated. Learners may confuse the words because in both cases someone experiences something negative. But 'Strafe' sounds like a rule and a consequence, while 'Rache' sounds like personal retaliation.

Aus Rache zerkratzte er das Fahrrad seines Nachbarn.
Out of revenge, he scratched his neighbor's bicycle.
Finns Strafe ist eine Woche ohne Handy, weil er wieder zu spät nach Hause kam.
Finn's punishment is a week without his phone because he came home late again.