Honor duels are a tradition that gained popularity first in the Oathlands. They were soon embraced by the Lyceum city-states, and eventually became the preferred method of dispute resolution across the Compact.
For your average insult or slight, a duel to first blood is proper. To kill one's opponent during an honor duel is considered a serious, nigh-unrecoverable stain upon one's honor, since the practice was adopted to prevent escalating bloodshed over perceived (or actual) slights.
Terms for a duel are worked out beforehand (IE how much damage will constitute 'first blood', whether certain weapons are disallowed/allowed, etc). In duels for honor OR duels for exhibition, such as a Rite to Gloria, it is appropriate to keep in mind the fight is for story, and realize that IC, no one would greet complaints of "but my opponent had better boots/axe/higher skill" with anything but scorn.
Note that trial by combat, while a right accused criminals can claim, is governed by a different set of rules.
(see also help files for "champions", "heirloom weapons", and "trial by combat")