The Epee is a direct descendant of the duelling sword, and epee fencing is probably the closest thing in the modern sport to actual duelling. An epee has a slightly heavier blade than the foil, and has a larger guard, needed because the hand is part of the target.

Indeed there are no target restrictions at all in epee, you are allowed to hit any part of the body. Also there is no concept of “priority”. The first fencer to score a hit gets the point. If both fencers hit at the same time (with in 1/25th of a second) they both get a point. Epee is the weapon used in the Modern Pentathlon sport.