In ancient near-Eastern and Middle Eastern law, such as Babylonian law, the concept of lex talionis, "an eye for eye, a tooth for a tooth" stood as a centerpiece of retributive justice.
In societies not bound by the rule of law, if a person was hurt, then the hurt person (or their relative) would take vengeful retribution on the person who caused the pain. Often the retibution would be much more than the crime; it often was death. Babylonian law put a limit on such actions, restricting the retribution to be no more than that crime.
In the Hebrew Bible, God issues many denunciations of ancient near-Eastern morality and law; the Torah (Exodus 21:24) offers its own statement of "an eye for an eye, a tooth for a tooth". Read in its historical context, this seems not be encouraging retributive justice, but is rather setting forth a commandment that punishments must be no more worse than the crime, giving as an example "an eye for eye, or a tooth for a tooth". This verse probably was meant to serve as a limitation on what kind of response the injured party could give.
Lex talionis in Judaism
The oral law of Judaism holds that this verse was never meant to be followed literally. The rabbis of the Talmud ask, "How can any person be certain that the punishment they inflict is definitely no worse than the initial injury?" They answer that this is impossible to carry out in practice. Therefore, they conclude that to follow the spirit of this law, it must be interpreted as applying to financial damages that are commesurate with the severity of the crime.
The Oral Law explains that what is meant is a sophisticated five-part monetary form of compensation, consisting of payment for "Damages, Pain, Medical Expenses, Incapacitation, and Mental Anguish" - which underlie many modern "advanced" legal codes? And the expression, "An eye for an eye, etc." means that that is what the perpetrator deserves, if not for the mercy of the Torah and its Author. Ah, you ask, how do you know the Torah means that, and is not to be taken literally? Because the Torah says, "Do not take a ransom for the life of a Murderer, who is wicked to the extent that he must die"; for the murderer, there is no monetary amount that is sufficient to grant him atonement in the eyes of God! Only payment with his life will secure that atonement! But for other forms of injury, we will take millions of dollars from the criminal, as a ransom for his eye, hand, or foot; and as atonement, hopefully rendering him a poor man, for his terrible crime! (Union of Orthodox Congregations website)
Another proof: Suppose a blind person damaged an eye of another. How do we perform "an eye for an eye"? (Babylonian Talmud, tractate Bava Kama 84a).
Criticisms
Most Christians see the New Testament as superior to the Hebrew Bible, and have traditionally read many of the laws in the Hebrew Bible as outdated or immoral. Outside of the Jewish community, the Christian view of the Hebrew Bible has become standard for many non-Christians. As such, many non-Christians have a critical view of the Hebrew Bible's conception of justice, and also of rabbinic Judaism's concept of justice. One example of this point of view is the quote "An eye for an eye leaves the whole world blind" by Mohandas Gandhi.
Those who disagree with this view note that it is a Christian interpretation of the commandment, which assumes that the directive encourages bloody retributive justice. Since the original intent was to limit retribution, the criticism is held to be misinformed and invalid.
See also: Turn the other cheek (the opposite)