עין תחת עין
שן תחת שן
An eye for an eye,
a tooth for a tooth… 
Possibly the single most misunderstood teaching of Torah!
(This will be a short discussion, in keeping with the format I’ve been trying to maintain in this blog. But I recommend looking at commentaries — in particular, the “Stone” chumash published by Art Scroll, and the “Hertz” chumash — for somewhat extended discussions of this topic.)
These words are usually taken to mean that retributive vengeance is “OK.” But anyone thinking clearly can quickly see the fallacy in that:
“‘An eye for an eye’ makes the whole world blind.” 
Put simply, this is a law of “restitution” rather than “retribution.” It’s about fair-ness, not revenge. If we’ve damaged a person’s property, we’re responsible for the value of the damage we’ve done. For example, if we’ve done $100 worth of damage, it’s insufficient for us to offer $10 and an “I’m sorry.”
If’ we’ve done damage to another’s person — to his or her body — we’re similarly responsible to compensate him or her for the value of the damage we’ve done. “An eye for an eye” doesn’t mean — and never meant — that we can claim in vengeance the eye of another person who might have damaged our own eye, or vice versa! It means — and has always meant — that we (or they) are entitled to fair compensation for what’s been lost.
We are morally, ethically and financially responsible for the damage we do. We can’t (or shouldn’t) “buy our way” out of it by giving less-than-adequate compensation.
We often hear about this today, with regard to someone being harmed in some way by the use of a product, or in the course of their work. If, for example, a person loses the use of an arm at work (assuming that it wasn’t because of any irresponsible behavior on their own part), is it adequate for the employer or the owner of the business to simply give 2-weeks severance pay to the worker who is no longer of use?
This is barely even a beginning to the discussion of this topic, but I offer it to make a simple point: Torah is not here talking about “revenge.” It’s talking about a fair standard of justice that’s applied to all — rich and poor — equally.
Think of it as being, in part, less about what others owe us (i.e. “revenge”) and more about what we owe others for harm or damage that results from our own action or inaction. Think of it also as stating that this law is to be applied to the rich and powerful equally with the poor and weak (one can easily imagine instances of injustice during the Egyptian bondage that might have given rise to the need for this).
In Christian scripture , this law is mentioned as being familiar to the Judean population of that time, the alternative being to “turn the other cheek.” The usual explanation is that “an eye for an eye” refers to harsh, “unloving” revenge, and “turning the other cheek” refers to a loving response (although this isn’t necessarily the only inference of the original statement).
However, if we understand “an eye for an eye” as meaning “just and fair com-pensation” (rather than revenge), “turning the other cheek” then would mean (at least): voluntarily foregoing that to which we’re fairly entitled. It doesn’t have to imply something intrinsically “harsh” or “unloving” in the original principle of “an eye for an eye.”
The Talmud likewise extols the one who foregoes recompense:
“All who overlook what’s done [or owed] to them, Heaven overlooks their sins in return.” 
But as spiritually praiseworthy as it might be for an individual to forego compensation, a society cannot long exist without justice at its core. Rabbi Shimon b. Gamliel said  that Justice (“Din;” “judgement”) is one of the three things on which the world itself stands. To this, Rabbi J.H. Hertz commented:
“Justice is truth in action, in contrast to lawless might [i.e. “might makes right”]. The tragedy of the Jew throughout history is that he [or she] has so often been denied justice. Let no Jew, therefore, deny justice to anyone; and never deprive anyone of life or health, honour or happiness. ” 
No Jew should do so — nor should anyone else in this world of G-d’s.