The 4-3 defensive front is a base defense consisting of four defensive linemen and three linebackers. The man credited with inventing the 4-3 at the professional level is Tom Landry, who coached the Dallas Cowboys from 1960-1988.
Landry developed an adaptation to the 4-3 known as the "Flex" defense (aka "Doomsday"). The Flex has a reputation for being one of the most confusing defenses in the history of football because it changed based on each offensive player's movement during the play.
Before the snap, the Flex looked like a wacky 4-3 scheme (keep in mind, this was on purpose, part of the Flex's charm was to confuse the offense as much as possible). The strong-side defensive tackle and weak-side defensive end back off the line of scrimmage a few steps and the linebackers creep up toward the line of scrimmage.
The Flex was developed to help the middle linebacker stay unblocked so he could make a play on the ball. All the other positions stayed in a pseudo-zone run defense, where they were expected to hold down their area and take up blockers, while also being ready to react to their opponent. Offsetting the defensive linemen at the line of scrimmage created channels for the MLB to shoot through into the backfield.
Despite its on-field success, few coaches ever used the Flex because of its difficulty. The mental strength required by the defense on every play was often greater than the physical requirements.