Avenge, revenge mean to inflict punishment on a person who has wronged oneself or another. Once close synonyms, these verbs are now increasingly divergent in implications.
One may avenge or revenge (oneself or another who is wronged), but avenge is to be preferred when the motive is a desire to vindicate or to serve the ends of justice or when one visits just or merited punishment on the wrongdoer.
On the other hand, one revenges oneself or, rarely, another when one inflicts injury on or upon an offender in a desire to exact satisfaction for his offense. Revenge may imply a desire for vindication or an aim to serve the ends of justice, but more often it suggests a desire to get even, to pay back in kind or degree, and therefore variously connotes malice, spite, or an unwillingness to forgive.
Also, one may either avenge or revenge a wrong or injury but avenge usually implies that the end is just retribution whether the activity is in one’s own or another’s behalf, whereas revenge implies that the end is retaliation and the compelling spirit of the act hatred or bitterness; thus, Orestes revenged his father’s murder by killing the murderess, his mother, but the gods avenged his matricide by driving him mad.