the act of harming or killing someone because they have done something bad to you 报复；报仇
Both sides were locked in a cycle of violence and vengeance. 双方陷入暴力和复仇的循环之中。
take/wreak/inflict vengeance on someone :
He was desperate to take vengeance on Marie's killer. 他不顾一切，一心想向杀害玛丽的凶手复仇。
Synonyms and related words
Revenge: revenge, vengeance, retribution...